SSB 201 – Sosyal Bilimler İçin İstatistik I

Final Sınavı

library (gapminder)
## Warning: package 'gapminder' was built under R version 4.5.2
library (dplyr)
## Warning: package 'dplyr' was built under R version 4.5.2
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library (ggplot2)

Soru 1 – Veri Setini İnceleme ve Düzenleme

1.a) gapminder veri setindeki değişken isimlerini ve veri türlerini inceleyiniz.

1.b) Aşağıdaki değişkenleri seçerek gapminder_tr isimli yeni bir veri seti oluşturunuz:

  • ulke (country)

  • yil (year)

  • yasam_beklentisi (lifeExp)

  • kisi_basi_gelir (gdpPercap)

  • kita (continent)

1.c) Bu yeni veri setindeki değişken adlarını Türkçeleştiriniz ve gapminder_tr üzerine kaydediniz.

Soru 2 – Betimsel İstatistikler

2.a) gapminder_tr veri seti için summary() fonksiyonunu kullanarak genel özeti elde ediniz.

2.b) Yaşam beklentisi değişkeninin ortalama, medyan ve ranj değerlerini açıklayınız.

Soru 3 – Frekans ve Yüzde Tablosu

Not: Aşağıdaki soruları gapminder_tr veri setini kullanarak yanıtlayın.

3.a) Kıta (continent) değişkenine ait frekans tablosunu oluşturunuz.

3.b) Aynı değişken için yüzde (%) dağılımını hesaplayınız.

Soru 4 – Saçılım Diyagramı ve Korelasyon

4.a) Yaşam beklentisi (lifeExp) ile kişi başına düşen gelir (gdpPercap) arasındaki ilişkiyi gösteren bir saçılım diyagramı oluşturunuz. Eksen adlarını ve grafiğin başlığını ekleyiniz.

4.b) Bu iki değişken arasındaki korelasyon katsayısını hesaplayınız ve korelasyon katsayısını yorumlayınız.

Soru 5 – Basit Doğrusal Regresyon

5.a) Kişi başına düşen gelirin (gdpPercap), yaşam beklentisini (lifeExp) yordayıp yordamadığını test eden bir basit doğrusal regresyon modeli kurunuz.

5.b) Regresyon çıktısından aşağıdaki bilgileri bulunuz ve yorumlayınız:

  • eğim (β₁)

  • kesişim (β₀)

  • R-kare (R²)

5.c) Yaşam beklentisi (yasam_beklentisi) ile kişi başına düşen gelir (kisi_basi_gelir) arasındaki ilişkiyi gösteren bir saçılım diyagramı oluşturunuz. Grafiğe uygun eksen adlarını ve bir başlık ekleyiniz. Bu grafiğin üzerine basit doğrusal regresyon çizgisini ekleyiniz.

Soru 6 - geom_jitter fonksiyonunun kullanım amacı nedir?

library(ggplot2)
library(gapminder)
data("gapminder")
names(gapminder)
## [1] "country"   "continent" "year"      "lifeExp"   "pop"       "gdpPercap"
glimpse(gapminder)
## Rows: 1,704
## Columns: 6
## $ country   <fct> "Afghanistan", "Afghanistan", "Afghanistan", "Afghanistan", …
## $ continent <fct> Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, …
## $ year      <int> 1952, 1957, 1962, 1967, 1972, 1977, 1982, 1987, 1992, 1997, …
## $ lifeExp   <dbl> 28.801, 30.332, 31.997, 34.020, 36.088, 38.438, 39.854, 40.8…
## $ pop       <int> 8425333, 9240934, 10267083, 11537966, 13079460, 14880372, 12…
## $ gdpPercap <dbl> 779.4453, 820.8530, 853.1007, 836.1971, 739.9811, 786.1134, …
gapminder_tr <-gapminder %>%
  rename(
    ülke = country,
    yıl = year,
    yasam_beklentisi = lifeExp,
    kisi_basi_gelir = gdpPercap,
    kita = continent,
  )
names(gapminder_tr)
## [1] "ülke"             "kita"             "yıl"              "yasam_beklentisi"
## [5] "pop"              "kisi_basi_gelir"
summary(gapminder_tr)
##           ülke            kita          yıl       yasam_beklentisi
##  Afghanistan:  12   Africa  :624   Min.   :1952   Min.   :23.60   
##  Albania    :  12   Americas:300   1st Qu.:1966   1st Qu.:48.20   
##  Algeria    :  12   Asia    :396   Median :1980   Median :60.71   
##  Angola     :  12   Europe  :360   Mean   :1980   Mean   :59.47   
##  Argentina  :  12   Oceania : 24   3rd Qu.:1993   3rd Qu.:70.85   
##  Australia  :  12                  Max.   :2007   Max.   :82.60   
##  (Other)    :1632                                                 
##       pop            kisi_basi_gelir   
##  Min.   :6.001e+04   Min.   :   241.2  
##  1st Qu.:2.794e+06   1st Qu.:  1202.1  
##  Median :7.024e+06   Median :  3531.8  
##  Mean   :2.960e+07   Mean   :  7215.3  
##  3rd Qu.:1.959e+07   3rd Qu.:  9325.5  
##  Max.   :1.319e+09   Max.   :113523.1  
## 
gapminder_tr <-gapminder_tr |>
  select(yasam_beklentisi) |>
  na.omit()

Yıl kategorisinde medyan=ortalama ranj=2007-1952=55 medyan ve ortalamanın birbirine eşit olması dağılımın simetrik olduğunu gösteriyor. Yasam_beklentisi kategorisinde medyan=60.71 ortalama=59.47 değerler birbirine cok yakin oldugu icin dagilim simetriktr diyebiliriz ranj=82.60-23.60=59.60 Kisi basi gelir ise ranj=113523.1-241.2=113281.9 medyan=3531.8 ortalama=7215.3 medyan<ortalama dağılım sağa çarpık yani pozitiftir

table(gapminder_tr$yasam_beklentisi)
## 
##   23.599   28.801       30   30.015   30.331   30.332    31.22   31.286 
##        1        1        1        1        1        1        1        1 
##    31.57   31.975   31.997   31.999   32.065     32.5   32.548   32.767 
##        1        1        1        1        1        1        1        1 
##   32.978   33.489   33.609   33.685   33.779   33.896    33.97       34 
##        1        1        1        1        1        1        1        1 
##    34.02   34.078   34.113   34.482   34.488   34.558   34.812   34.906 
##        1        1        1        1        1        1        1        1 
##   34.977    35.18   35.307     35.4   35.463   35.492   35.753   35.857 
##        1        1        1        1        1        1        1        1 
##   35.928   35.983   35.985   36.087   36.088   36.157   36.161   36.256 
##        1        1        1        1        1        1        1        1 
##   36.319   36.324   36.486   36.667   36.681   36.788   36.936   36.981 
##        1        1        1        1        1        1        1        1 
##   36.984   37.003   37.197   37.207   37.278   37.328   37.373   37.444 
##        1        1        1        1        1        1        1        1 
##   37.464   37.465   37.468   37.484   37.485   37.578   37.579   37.686 
##        1        1        1        1        1        1        1        1 
##   37.802   37.814   37.928   38.047   38.092   38.113   38.223   38.308 
##        1        1        1        1        1        1        1        1 
##   38.333    38.41   38.438   38.445    38.48   38.487   38.523   38.596 
##        1        1        1        1        1        1        1        1 
##   38.598   38.635   38.842   38.865   38.977   38.987   38.999   39.031 
##        1        1        1        1        1        1        1        1 
##   39.143   39.193   39.327   39.329   39.348    39.36   39.393   39.417 
##        1        1        1        1        1        1        1        1 
##   39.475   39.483   39.486   39.487   39.613   39.624   39.658   39.693 
##        1        1        1        2        1        1        1        1 
##   39.848   39.854   39.875   39.881   39.897   39.906   39.918   39.942 
##        1        1        1        1        1        1        1        1 
##   39.977   39.978   39.989       40   40.006   40.059    40.08   40.118 
##        1        1        1        1        1        1        1        1 
##   40.158   40.238   40.249   40.317   40.328   40.358   40.412   40.414 
##        1        1        1        1        1        1        1        1 
##   40.428   40.477   40.489   40.502   40.516   40.533   40.543   40.546 
##        1        1        1        1        1        1        1        1 
##   40.647   40.652   40.696   40.697   40.715   40.762   40.802   40.822 
##        1        1        1        1        1        1        1        1 
##   40.848    40.87   40.963   40.973   41.003   41.012    41.04   41.208 
##        1        1        1        1        1        1        1        1 
##   41.215   41.216   41.245   41.291   41.366   41.407   41.454   41.472 
##        1        1        1        1        1        1        1        1 
##   41.478     41.5   41.536   41.674   41.714   41.716   41.725   41.763 
##        1        1        1        1        1        1        1        1 
##   41.766   41.842    41.89   41.893   41.905   41.912   41.974   42.023 
##        1        1        1        1        1        1        1        1 
##   42.024   42.038   42.045   42.074   42.082   42.111   42.115   42.122 
##        1        1        1        1        1        1        1        1 
##   42.129   42.138   42.189   42.221   42.244    42.27   42.314   42.338 
##        1        1        1        1        1        1        1        1 
##   42.384    42.46   42.469   42.495   42.518   42.568   42.571   42.587 
##        1        1        1        1        1        1        1        1 
##   42.592   42.598   42.614   42.618   42.643   42.723   42.731   42.795 
##        1        1        1        1        1        1        1        1 
##   42.821   42.858   42.861   42.868   42.873   42.881   42.887   42.891 
##        1        1        1        1        1        1        1        1 
##   42.955   42.974       43   43.077   43.149   43.158    43.16   43.165 
##        1        1        1        1        1        1        1        1 
##   43.266   43.308   43.413   43.415   43.424   43.428   43.436   43.453 
##        1        1        1        1        1        1        1        1 
##   43.457   43.487   43.515   43.548   43.563   43.585    43.59   43.591 
##        1        1        1        1        1        1        1        1 
##   43.601   43.605   43.662   43.753   43.764   43.767   43.795   43.828 
##        1        1        1        1        1        1        1        1 
##   43.869    43.89   43.902   43.916   43.922   43.971       44    44.02 
##        1        1        1        1        1        1        1        1 
##   44.026   44.056   44.057   44.077     44.1   44.142   44.175   44.246 
##        1        1        1        1        1        2        1        1 
##   44.248   44.284   44.366   44.444   44.467   44.501 44.50136    44.51 
##        1        1        1        1        1        1        1        1 
##   44.514   44.535   44.555   44.578   44.593   44.598     44.6   44.665 
##        1        1        1        1        1        1        2        1 
##   44.686   44.736   44.741   44.779   44.799   44.851   44.852   44.869 
##        1        1        1        1        1        1        1        1 
##   44.873   44.885   44.916    44.93   44.966   44.992       45   45.009 
##        1        1        1        1        1        1        1        2 
##   45.032   45.047   45.053   45.083   45.108   45.226   45.248   45.252 
##        1        1        1        1        1        1        1        1 
##   45.262   45.289    45.32   45.326   45.344   45.363   45.415   45.423 
##        1        1        1        1        1        1        1        1 
##   45.432   45.504   45.548   45.552   45.557   45.569    45.58   45.642 
##        1        1        1        1        1        1        1        1 
##   45.664   45.669   45.671   45.678   45.685   45.757   45.815   45.826 
##        1        1        1        1        1        1        1        1 
##   45.883    45.91   45.914   45.928   45.936   45.964   45.989   46.023 
##        1        1        1        1        1        1        1        1 
##   46.027   46.066     46.1   46.137   46.218   46.242   46.243   46.263 
##        1        1        1        1        1        1        1        1 
##   46.289   46.344   46.364   46.388   46.452   46.453   46.462   46.471 
##        1        1        1        1        1        1        1        1 
##   46.472   46.519   46.608   46.633   46.634   46.684   46.714   46.748 
##        1        1        1        1        1        1        1        1 
##   46.769   46.775   46.809   46.832   46.859   46.881   46.886   46.923 
##        1        1        1        1        1        1        1        1 
##   46.954   46.988   46.992   47.014   47.049     47.1   47.181   47.193 
##        1        1        1        1        1        1        1        1 
##    47.35    47.36   47.383   47.391   47.412   47.453   47.457   47.464 
##        1        1        1        1        1        1        1        1 
##   47.471   47.472   47.495   47.545    47.62   47.622    47.67   47.747 
##        1        1        1        1        1        1        1        1 
##   47.752   47.768   47.784     47.8   47.804   47.808   47.813   47.838 
##        1        1        1        1        1        1        1        1 
##   47.924   47.949   47.985   47.991   48.041   48.042   48.051   48.072 
##        1        1        1        1        1        1        1        1 
##   48.079   48.091   48.122   48.126   48.127   48.159   48.211   48.245 
##        1        1        1        1        1        1        1        1 
##   48.251   48.284   48.295   48.303   48.328   48.357   48.386   48.388 
##        1        1        1        2        1        1        1        1 
##   48.435   48.437   48.451   48.463   48.466   48.492    48.57   48.576 
##        1        2        1        1        1        1        1        1 
##   48.632    48.69   48.812   48.825   48.879   48.944   48.945   48.969 
##        1        1        1        1        1        1        1        1 
##   49.096   49.113    49.19   49.203   49.265   49.293   49.325   49.339 
##        1        1        1        1        1        1        1        1 
##   49.348    49.35   49.355   49.379   49.396   49.402    49.42   49.517 
##        1        1        1        1        1        1        1        1 
##   49.552   49.557   49.579    49.58   49.594   49.618   49.651   49.759 
##        1        1        1        1        1        1        1        1 
##   49.767     49.8   49.801   49.828   49.849   49.856   49.875   49.901 
##        1        1        1        1        1        1        1        1 
##   49.903   49.919   49.923   49.951   49.991   50.009   50.016   50.023 
##        1        1        1        1        1        1        1        1 
##    50.04   50.056   50.107   50.227   50.254    50.26   50.305   50.324 
##        1        1        1        1        1        1        1        1 
##   50.335   50.338    50.35    50.43    50.44   50.469   50.485   50.525 
##        1        1        1        1        1        1        1        1 
## 50.54896   50.608   50.643    50.65   50.651   50.654   50.725   50.728 
##        1        1        1        1        2        1        1        1 
##   50.789   50.821   50.848   50.852   50.904   50.917   50.924   50.939 
##        1        1        1        1        1        1        1        2 
##   50.957   50.986   50.992   51.016   51.051   51.137   51.159   51.253 
##        1        1        1        1        1        1        1        1 
##   51.313   51.334   51.356   51.386   51.407   51.445   51.455   51.457 
##        1        1        1        1        1        1        1        1 
##   51.461   51.479   51.509    51.52   51.535   51.542   51.573   51.579 
##        1        1        1        1        1        1        1        1 
##   51.604   51.629   51.631   51.724   51.744   51.756   51.818   51.821 
##        1        1        1        1        1        1        1        1 
##   51.884   51.893   51.927   51.929    52.04   52.044   52.053   52.098 
##        1        1        1        1        1        1        1        1 
##   52.102   52.143   52.199   52.208   52.214   52.295   52.307   52.337 
##        1        1        1        1        1        1        1        1 
##   52.358   52.374   52.379   52.469   52.517   52.537   52.556   52.644 
##        1        1        1        1        1        2        1        1 
##   52.681   52.702   52.724   52.773    52.79   52.819   52.862   52.887 
##        1        1        1        1        1        1        1        1 
##   52.906   52.922   52.933   52.947   52.961   52.962    52.97    53.07 
##        1        1        1        1        1        1        1        1 
##   53.157   53.285   53.298   53.319   53.365   53.373   53.378   53.459 
##        1        1        1        1        1        1        1        1 
##   53.556   53.559   53.599    53.63   53.636   53.655   53.676   53.696 
##        1        1        1        1        1        1        1        1 
##   53.738   53.744   53.754    53.82   53.832   53.859   53.867   53.884 
##        1        1        1        1        1        1        1        1 
##   53.886   53.914   53.919   53.983   53.995   54.043   54.081    54.11 
##        1        1        1        1        1        1        1        1 
##   54.208   54.289   54.314   54.336   54.406   54.407   54.425   54.459 
##        1        1        1        1        1        1        1        1 
##   54.467   54.496   54.518    54.64   54.655   54.745   54.757   54.777 
##        1        1        1        1        1        1        1        1 
##   54.791   54.907   54.926   54.978   54.985   55.078   55.088   55.089 
##        1        1        1        1        1        1        1        1 
##    55.09   55.118   55.151    55.19   55.191    55.23   55.234    55.24 
##        1        1        1        1        1        1        1        1 
##   55.292   55.322   55.373   55.448   55.471   55.491   55.527   55.558 
##        1        1        1        1        1        1        1        1 
##   55.561   55.565   55.599   55.602   55.625   55.635   55.665   55.727 
##        1        1        1        1        1        1        1        1 
##   55.729    55.73   55.737   55.764   55.769   55.803   55.855   55.861 
##        1        1        1        1        1        1        1        1 
##   55.928   56.006   56.007   56.018   56.024   56.029   56.059   56.061 
##        1        1        1        1        1        1        1        1 
##   56.074   56.145   56.155   56.158   56.159   56.369   56.393   56.433 
##        1        1        1        1        1        1        1        1 
##   56.437    56.48   56.528   56.532   56.534   56.564   56.596   56.604 
##        1        1        1        1        1        1        1        1 
##   56.656   56.671   56.678   56.695   56.696   56.728   56.735   56.751 
##        1        1        1        1        1        1        1        1 
##   56.752   56.761   56.867   56.923   56.941    56.95   57.005   57.046 
##        1        1        1        1        1        1        1        1 
##    57.18   57.206   57.251   57.286   57.296   57.367   57.402   57.442 
##        1        1        1        1        1        1        1        1 
##    57.47   57.489   57.501   57.561   57.593   57.632   57.666   57.674 
##        2        1        1        1        1        1        1        1 
##   57.678   57.702   57.716   57.863   57.907   57.924   57.939   57.996 
##        1        1        1        1        1        1        1        1 
##   58.014    58.02   58.033    58.04   58.041   58.056   58.061   58.065 
##        1        1        1        1        1        1        1        1 
##   58.089   58.137   58.161   58.196   58.207   58.245   58.285   58.299 
##        1        2        1        1        1        1        1        1 
##   58.333   58.339 58.38112    58.39    58.42   58.447    58.45   58.453 
##        1        1        1        1        1        1        1        1 
##   58.474     58.5    58.53    58.55   58.553   58.556    58.69   58.766 
##        1        1        1        1        1        2        1        1 
##   58.796   58.811   58.816   58.909   58.968     59.1   59.164   59.201 
##        1        1        1        1        1        1        1        1 
##    59.28   59.285   59.298   59.319    59.32   59.339   59.371   59.412 
##        1        1        1        1        1        1        1        1 
##   59.421   59.426   59.443   59.448   59.461   59.489   59.504   59.507 
##        1        1        1        1        1        1        1        1 
##   59.545     59.6    59.62   59.631    59.65   59.685   59.723   59.797 
##        1        1        1        1        1        1        1        1 
##    59.82   59.837   59.908   59.923   59.942   59.957   59.963   60.022 
##        1        1        1        1        1        1        1        1 
##   60.026    60.06    60.11   60.137   60.187    60.19   60.222   60.223 
##        1        1        1        1        1        1        1        1 
##   60.236   60.246   60.308   60.328   60.351   60.363   60.377   60.396 
##        1        1        1        1        1        1        1        1 
##   60.405   60.413    60.43   60.461    60.47   60.523   60.542    60.66 
##        1        1        1        1        1        1        1        1 
##   60.765    60.77   60.782   60.834   60.835   60.838   60.909   60.916 
##        1        1        1        1        1        1        1        1 
##    60.96   61.036    61.05   61.134   61.195    61.21   61.271    61.31 
##        1        1        1        1        1        1        1        2 
##    61.34   61.366   61.368   61.406   61.448   61.456   61.484   61.489 
##        1        1        1        1        1        1        1        1 
##    61.51   61.557     61.6   61.623   61.685   61.728   61.765   61.788 
##        1        1        1        1        1        1        1        1 
##     61.8   61.817   61.818   61.888    61.93   61.999   62.008   62.013 
##        1        1        1        1        1        1        1        1 
##   62.038    62.05   62.069   62.082   62.094   62.155   62.192   62.247 
##        1        1        1        1        1        1        1        1 
##   62.325   62.351   62.361     62.4   62.485   62.494    62.61   62.612 
##        1        1        1        1        1        1        1        1 
##   62.649   62.677   62.681   62.698   62.728   62.742   62.745    62.82 
##        1        1        1        1        1        1        1        1 
##   62.842   62.879   62.944   62.974    63.01   63.012    63.03    63.04 
##        1        1        1        1        1        1        1        1 
##   63.062   63.108 63.11888   63.154   63.179   63.196     63.3   63.306 
##        1        1        1        1        1        1        1        1 
##   63.336   63.373   63.441   63.479    63.61   63.622   63.625   63.674 
##        1        1        1        1        1        1        1        1 
##   63.727   63.728   63.739   63.785   63.837    63.87   63.883 63.96736 
##        1        1        1        1        1        1        1        1 
##   63.983    64.03   64.048   64.062   64.071     64.1   64.134   64.151 
##        1        1        1        1        1        1        1        1 
##   64.164   64.266   64.274    64.28   64.337   64.342    64.36   64.361 
##        1        1        1        1        1        1        1        1 
##    64.39   64.399   64.406   64.492   64.531    64.59   64.597   64.624 
##        1        1        1        1        1        1        1        1 
##   64.698    64.75   64.766    64.77    64.79    64.82     64.9    64.93 
##        1        1        1        1        1        1        1        1 
##    64.94   64.951   65.032   65.033   65.042   65.044   65.142   65.152 
##        1        1        1        1        1        1        1        1 
##     65.2   65.205   65.246   65.256    65.39   65.393     65.4   65.421 
##        1        1        1        1        1        1        1        1 
##   65.424   65.483     65.5   65.525   65.528   65.554    65.57   65.593 
##        1        1        1        1        1        1        1        1 
##    65.61   65.634   65.712   65.742    65.77   65.798   65.799   65.815 
##        1        1        1        1        1        1        1        1 
##   65.843    65.86   65.869     65.9    65.94   65.949   66.041   66.046 
##        1        1        1        1        1        1        1        1 
##   66.071   66.084   66.099   66.146   66.216    66.22   66.234   66.295 
##        1        1        1        1        1        1        1        1 
##   66.322   66.353   66.399    66.41   66.458    66.55     66.6    66.61 
##        1        1        1        1        2        1        1        1 
##   66.653    66.66   66.662   66.711   66.798     66.8   66.803    66.87 
##        1        1        1        1        1        3        1        1 
##   66.874   66.894    66.91   66.914   66.974   66.983   67.044   67.046 
##        1        1        1        1        1        1        1        1 
##   67.052   67.057   67.064   67.065   67.123    67.13   67.159   67.178 
##        1        1        1        1        1        1        1        1 
##   67.217   67.231   67.274   67.297   67.298   67.378   67.405    67.41 
##        1        1        1        1        1        1        1        1 
##    67.45   67.456    67.48    67.49     67.5    67.51   67.521    67.64 
##        2        1        1        1        2        1        1        1 
##    67.65   67.659    67.66   67.662    67.69   67.712   67.727   67.734 
##        1        1        1        1        1        1        1        1 
##   67.744   67.768    67.81    67.84   67.849    67.85    67.86   67.926 
##        1        1        1        1        1        1        1        1 
##   67.946    67.96       68   68.015   68.042   68.225   68.253    68.29 
##        1        1        2        1        1        1        1        1 
##     68.3   68.386   68.421   68.426    68.44   68.457   68.468   68.481 
##        1        1        1        1        1        1        1        1 
##     68.5    68.54   68.557   68.564   68.565   68.588   68.673   68.681 
##        1        1        1        2        1        1        1        1 
##    68.69     68.7    68.73    68.74    68.75   68.755   68.757   68.768 
##        1        1        1        1        2        1        1        1 
##   68.832   68.835     68.9    68.93   68.976   68.978       69   69.011 
##        1        1        1        2        1        1        1        1 
##    69.03   69.052     69.1    69.12    69.15   69.152    69.17    69.18 
##        1        1        2        1        1        1        1        2 
##    69.21    69.24   69.249    69.26   69.292   69.343    69.36   69.388 
##        1        2        1        1        1        1        1        1 
##    69.39     69.4   69.451    69.46   69.465   69.481    69.49   69.498 
##        4        1        1        1        1        1        1        1 
##     69.5    69.51   69.521    69.53   69.535    69.54    69.58   69.582 
##        2        2        1        1        1        1        1        1 
##    69.61   69.613   69.615    69.62    69.66    69.69   69.718    69.72 
##        2        1        1        2        1        1        1        1 
##   69.745    69.76   69.772   69.806    69.81   69.819    69.82    69.83 
##        1        1        1        1        1        1        1        1 
##    69.86   69.862   69.885     69.9   69.906   69.942    69.95   69.957 
##        1        1        1        1        1        1        1        1 
##    69.96   69.978       70   70.001    70.11    70.14   70.162    70.19 
##        1        1        1        1        1        1        1        1 
##   70.198    70.21    70.25   70.259    70.26   70.265    70.29     70.3 
##        1        1        1        1        1        1        2        2 
##   70.303   70.313    70.32    70.33    70.35   70.379    70.38    70.41 
##        1        1        1        2        1        1        1        1 
##    70.42   70.426    70.45   70.457    70.46   70.472    70.51   70.533 
##        3        1        1        1        1        1        1        1 
##    70.56   70.565    70.59   70.616    70.63   70.636    70.64   70.647 
##        1        1        1        1        1        1        1        1 
##    70.65    70.67   70.672    70.69   70.693    70.71   70.723   70.734 
##        1        1        1        1        1        1        1        1 
##   70.736    70.75   70.755    70.76   70.774    70.78   70.795     70.8 
##        1        3        1        2        1        1        1        2 
##   70.805    70.81   70.815   70.836   70.845   70.847    70.85    70.87 
##        1        1        1        1        1        1        1        1 
##     70.9    70.93    70.94    70.96   70.964    70.97    70.98    70.99 
##        1        1        1        1        1        1        2        1 
##   70.994       71   71.006   71.028    71.04    71.06   71.063    71.08 
##        1        2        1        1        1        1        1        3 
##   71.096     71.1    71.14    71.15   71.164    71.19   71.197    71.21 
##        1        2        1        1        1        1        1        1 
##   71.218    71.24   71.263    71.28     71.3   71.309    71.32   71.322 
##        1        1        1        1        1        1        2        1 
##   71.338    71.34    71.36    71.38   71.421    71.43    71.44   71.455 
##        1        2        1        1        1        1        2        1 
##    71.52   71.523   71.527    71.55   71.555    71.58   71.581   71.626 
##        2        1        1        1        1        1        1        1 
##    71.63   71.659   71.682   71.688   71.752    71.76   71.766    71.77 
##        1        1        1        1        1        1        1        1 
##   71.777    71.81    71.86   71.868   71.878    71.89   71.913   71.918 
##        1        1        1        1        1        1        1        1 
##    71.93   71.938   71.954   71.973   71.993       72    72.01   72.028 
##        1        1        1        1        1        2        1        1 
##    72.03   72.047    72.13    72.14   72.146    72.16    72.17   72.178 
##        1        1        2        1        1        2        1        1 
##    72.19    72.22   72.232   72.235   72.244    72.25   72.262   72.301 
##        1        1        1        1        1        1        1        1 
##   72.312    72.34    72.35    72.37    72.38    72.39   72.396     72.4 
##        1        1        1        1        1        1        1        1 
##   72.462   72.476    72.49   72.492   72.499     72.5    72.52   72.527 
##        1        1        2        1        1        1        1        1 
##   72.535   72.567    72.59   72.601   72.649    72.67    72.71   72.737 
##        1        1        1        1        1        1        1        1 
##    72.75   72.752    72.76   72.766    72.77   72.777     72.8   72.801 
##        1        1        1        1        2        1        1        1 
##    72.88   72.889   72.899    72.95    72.96   72.961    72.99   73.005 
##        1        1        1        1        1        1        1        1 
##   73.017   73.042   73.044   73.053    73.06   73.066     73.1    73.18 
##        1        1        1        1        2        1        1        1 
##   73.213    73.23   73.244   73.275   73.338    73.37    73.38     73.4 
##        1        1        1        1        1        1        1        1 
##    73.42   73.422    73.44    73.45    73.47    73.48    73.49    73.56 
##        1        1        2        1        3        1        1        1 
##     73.6   73.615    73.64    73.67    73.68   73.717    73.73   73.738 
##        1        1        1        1        3        1        1        1 
##   73.747    73.75    73.78     73.8    73.82    73.83    73.84   73.911 
##        1        2        1        2        1        1        1        1 
##   73.923   73.925    73.93   73.952   73.981   74.002    74.01    74.04 
##        1        1        1        1        1        1        1        1 
##    74.06    74.08    74.09   74.101   74.126   74.143    74.16   74.173 
##        1        1        1        1        1        1        1        1 
##   74.174   74.193    74.21   74.223   74.241   74.249    74.26    74.32 
##        2        1        1        1        1        1        1        1 
##    74.34    74.36    74.39   74.414    74.45    74.46   74.543    74.55 
##        2        1        1        1        1        1        1        1 
##    74.63   74.647    74.65   74.663    74.67    74.69   74.712    74.72 
##        2        1        1        1        1        1        1        1 
##    74.74   74.752   74.772   74.795     74.8    74.83   74.847   74.852 
##        1        1        1        1        1        1        1        1 
##    74.86   74.865   74.876    74.89   74.902   74.917    74.94    74.98 
##        1        1        1        1        1        1        1        1 
##   74.994   75.007    75.02    75.13    75.19    75.24    75.25   75.307 
##        1        1        1        1        1        2        1        1 
##    75.32    75.33    75.35    75.37    75.38    75.39   75.435    75.44 
##        1        1        1        1        1        1        1        1 
##   75.445    75.45   75.467    75.51   75.537   75.563     75.6   75.635 
##        1        1        1        1        1        1        1        1 
##    75.64   75.651     75.7   75.713   75.744   75.748    75.76   75.788 
##        1        1        1        1        1        1        1        1 
##   75.816    75.89    75.97    76.04    76.05    76.07    76.09    76.11 
##        1        1        2        1        1        1        1        2 
##   76.122   76.151   76.156   76.195     76.2    76.21     76.3    76.32 
##        1        1        1        1        1        1        1        1 
##    76.33    76.34   76.384    76.42   76.423   76.442    76.46   76.486 
##        1        1        1        3        1        1        1        1 
##    76.66    76.67    76.81    76.83    76.86     76.9   76.904    76.93 
##        1        1        1        1        1        1        1        1 
##    76.99    77.03   77.045    77.11    77.13   77.158    77.18    77.19 
##        2        1        1        1        1        2        1        1 
##   77.218    77.23    77.26    77.29    77.31    77.32    77.34    77.41 
##        1        1        1        1        1        1        1        1 
##    77.42    77.44    77.46    77.51    77.53    77.55    77.56    77.57 
##        1        1        1        1        1        1        1        1 
##   77.588   77.601   77.778   77.783    77.86   77.869   77.926    77.95 
##        1        1        1        1        1        1        1        1 
##    78.03   78.098   78.123    78.16   78.242   78.256   78.269   78.273 
##        2        1        1        1        1        1        1        1 
##    78.32   78.332    78.37     78.4   78.471    78.53   78.553    78.61 
##        2        1        1        1        1        1        1        1 
##   78.623    78.64    78.67   78.746    78.77   78.782    78.82    78.83 
##        1        1        2        1        3        1        1        1 
##   78.885    78.95    78.98    79.05    79.11   79.313    79.36    79.37 
##        1        1        1        1        1        1        1        1 
##    79.39   79.406   79.425   79.441   79.483    79.59   79.696   79.762 
##        1        1        1        1        1        1        1        1 
##    79.77    79.78   79.829   79.972       80    80.04   80.196   80.204 
##        1        1        1        1        1        1        1        1 
##    80.24    80.37     80.5   80.546    80.62   80.653   80.657    80.69 
##        1        1        1        1        1        1        1        1 
##   80.745   80.884   80.941   81.235   81.495   81.701   81.757       82 
##        1        1        1        1        1        1        1        1 
##   82.208   82.603 
##        1        1
prop.table((table(gapminder_tr$yasam_beklentisi)))
## 
##       23.599       28.801           30       30.015       30.331       30.332 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        31.22       31.286        31.57       31.975       31.997       31.999 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       32.065         32.5       32.548       32.767       32.978       33.489 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       33.609       33.685       33.779       33.896        33.97           34 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        34.02       34.078       34.113       34.482       34.488       34.558 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       34.812       34.906       34.977        35.18       35.307         35.4 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       35.463       35.492       35.753       35.857       35.928       35.983 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       35.985       36.087       36.088       36.157       36.161       36.256 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       36.319       36.324       36.486       36.667       36.681       36.788 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       36.936       36.981       36.984       37.003       37.197       37.207 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       37.278       37.328       37.373       37.444       37.464       37.465 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       37.468       37.484       37.485       37.578       37.579       37.686 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       37.802       37.814       37.928       38.047       38.092       38.113 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       38.223       38.308       38.333        38.41       38.438       38.445 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        38.48       38.487       38.523       38.596       38.598       38.635 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       38.842       38.865       38.977       38.987       38.999       39.031 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       39.143       39.193       39.327       39.329       39.348        39.36 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       39.393       39.417       39.475       39.483       39.486       39.487 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 
##       39.613       39.624       39.658       39.693       39.848       39.854 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       39.875       39.881       39.897       39.906       39.918       39.942 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       39.977       39.978       39.989           40       40.006       40.059 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        40.08       40.118       40.158       40.238       40.249       40.317 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       40.328       40.358       40.412       40.414       40.428       40.477 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       40.489       40.502       40.516       40.533       40.543       40.546 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       40.647       40.652       40.696       40.697       40.715       40.762 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       40.802       40.822       40.848        40.87       40.963       40.973 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       41.003       41.012        41.04       41.208       41.215       41.216 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       41.245       41.291       41.366       41.407       41.454       41.472 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       41.478         41.5       41.536       41.674       41.714       41.716 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       41.725       41.763       41.766       41.842        41.89       41.893 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       41.905       41.912       41.974       42.023       42.024       42.038 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       42.045       42.074       42.082       42.111       42.115       42.122 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       42.129       42.138       42.189       42.221       42.244        42.27 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       42.314       42.338       42.384        42.46       42.469       42.495 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       42.518       42.568       42.571       42.587       42.592       42.598 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       42.614       42.618       42.643       42.723       42.731       42.795 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       42.821       42.858       42.861       42.868       42.873       42.881 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       42.887       42.891       42.955       42.974           43       43.077 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       43.149       43.158        43.16       43.165       43.266       43.308 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       43.413       43.415       43.424       43.428       43.436       43.453 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       43.457       43.487       43.515       43.548       43.563       43.585 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        43.59       43.591       43.601       43.605       43.662       43.753 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       43.764       43.767       43.795       43.828       43.869        43.89 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       43.902       43.916       43.922       43.971           44        44.02 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       44.026       44.056       44.057       44.077         44.1       44.142 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 
##       44.175       44.246       44.248       44.284       44.366       44.444 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       44.467       44.501     44.50136        44.51       44.514       44.535 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       44.555       44.578       44.593       44.598         44.6       44.665 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 
##       44.686       44.736       44.741       44.779       44.799       44.851 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       44.852       44.869       44.873       44.885       44.916        44.93 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       44.966       44.992           45       45.009       45.032       45.047 
## 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 
##       45.053       45.083       45.108       45.226       45.248       45.252 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       45.262       45.289        45.32       45.326       45.344       45.363 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       45.415       45.423       45.432       45.504       45.548       45.552 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       45.557       45.569        45.58       45.642       45.664       45.669 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       45.671       45.678       45.685       45.757       45.815       45.826 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       45.883        45.91       45.914       45.928       45.936       45.964 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       45.989       46.023       46.027       46.066         46.1       46.137 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       46.218       46.242       46.243       46.263       46.289       46.344 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       46.364       46.388       46.452       46.453       46.462       46.471 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       46.472       46.519       46.608       46.633       46.634       46.684 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       46.714       46.748       46.769       46.775       46.809       46.832 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       46.859       46.881       46.886       46.923       46.954       46.988 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       46.992       47.014       47.049         47.1       47.181       47.193 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        47.35        47.36       47.383       47.391       47.412       47.453 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       47.457       47.464       47.471       47.472       47.495       47.545 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        47.62       47.622        47.67       47.747       47.752       47.768 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       47.784         47.8       47.804       47.808       47.813       47.838 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       47.924       47.949       47.985       47.991       48.041       48.042 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       48.051       48.072       48.079       48.091       48.122       48.126 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       48.127       48.159       48.211       48.245       48.251       48.284 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       48.295       48.303       48.328       48.357       48.386       48.388 
## 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       48.435       48.437       48.451       48.463       48.466       48.492 
## 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        48.57       48.576       48.632        48.69       48.812       48.825 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       48.879       48.944       48.945       48.969       49.096       49.113 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        49.19       49.203       49.265       49.293       49.325       49.339 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       49.348        49.35       49.355       49.379       49.396       49.402 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        49.42       49.517       49.552       49.557       49.579        49.58 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       49.594       49.618       49.651       49.759       49.767         49.8 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       49.801       49.828       49.849       49.856       49.875       49.901 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       49.903       49.919       49.923       49.951       49.991       50.009 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       50.016       50.023        50.04       50.056       50.107       50.227 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       50.254        50.26       50.305       50.324       50.335       50.338 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        50.35        50.43        50.44       50.469       50.485       50.525 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##     50.54896       50.608       50.643        50.65       50.651       50.654 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 
##       50.725       50.728       50.789       50.821       50.848       50.852 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       50.904       50.917       50.924       50.939       50.957       50.986 
## 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 
##       50.992       51.016       51.051       51.137       51.159       51.253 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       51.313       51.334       51.356       51.386       51.407       51.445 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       51.455       51.457       51.461       51.479       51.509        51.52 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       51.535       51.542       51.573       51.579       51.604       51.629 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       51.631       51.724       51.744       51.756       51.818       51.821 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       51.884       51.893       51.927       51.929        52.04       52.044 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       52.053       52.098       52.102       52.143       52.199       52.208 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       52.214       52.295       52.307       52.337       52.358       52.374 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       52.379       52.469       52.517       52.537       52.556       52.644 
## 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 
##       52.681       52.702       52.724       52.773        52.79       52.819 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       52.862       52.887       52.906       52.922       52.933       52.947 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       52.961       52.962        52.97        53.07       53.157       53.285 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       53.298       53.319       53.365       53.373       53.378       53.459 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       53.556       53.559       53.599        53.63       53.636       53.655 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       53.676       53.696       53.738       53.744       53.754        53.82 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       53.832       53.859       53.867       53.884       53.886       53.914 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       53.919       53.983       53.995       54.043       54.081        54.11 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       54.208       54.289       54.314       54.336       54.406       54.407 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       54.425       54.459       54.467       54.496       54.518        54.64 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       54.655       54.745       54.757       54.777       54.791       54.907 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       54.926       54.978       54.985       55.078       55.088       55.089 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        55.09       55.118       55.151        55.19       55.191        55.23 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       55.234        55.24       55.292       55.322       55.373       55.448 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       55.471       55.491       55.527       55.558       55.561       55.565 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       55.599       55.602       55.625       55.635       55.665       55.727 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       55.729        55.73       55.737       55.764       55.769       55.803 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       55.855       55.861       55.928       56.006       56.007       56.018 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       56.024       56.029       56.059       56.061       56.074       56.145 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       56.155       56.158       56.159       56.369       56.393       56.433 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       56.437        56.48       56.528       56.532       56.534       56.564 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       56.596       56.604       56.656       56.671       56.678       56.695 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       56.696       56.728       56.735       56.751       56.752       56.761 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       56.867       56.923       56.941        56.95       57.005       57.046 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        57.18       57.206       57.251       57.286       57.296       57.367 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       57.402       57.442        57.47       57.489       57.501       57.561 
## 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 
##       57.593       57.632       57.666       57.674       57.678       57.702 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       57.716       57.863       57.907       57.924       57.939       57.996 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       58.014        58.02       58.033        58.04       58.041       58.056 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       58.061       58.065       58.089       58.137       58.161       58.196 
## 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 
##       58.207       58.245       58.285       58.299       58.333       58.339 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##     58.38112        58.39        58.42       58.447        58.45       58.453 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       58.474         58.5        58.53        58.55       58.553       58.556 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 
##        58.69       58.766       58.796       58.811       58.816       58.909 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       58.968         59.1       59.164       59.201        59.28       59.285 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       59.298       59.319        59.32       59.339       59.371       59.412 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       59.421       59.426       59.443       59.448       59.461       59.489 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       59.504       59.507       59.545         59.6        59.62       59.631 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        59.65       59.685       59.723       59.797        59.82       59.837 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       59.908       59.923       59.942       59.957       59.963       60.022 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       60.026        60.06        60.11       60.137       60.187        60.19 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       60.222       60.223       60.236       60.246       60.308       60.328 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       60.351       60.363       60.377       60.396       60.405       60.413 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        60.43       60.461        60.47       60.523       60.542        60.66 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       60.765        60.77       60.782       60.834       60.835       60.838 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       60.909       60.916        60.96       61.036        61.05       61.134 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       61.195        61.21       61.271        61.31        61.34       61.366 
## 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 
##       61.368       61.406       61.448       61.456       61.484       61.489 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        61.51       61.557         61.6       61.623       61.685       61.728 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       61.765       61.788         61.8       61.817       61.818       61.888 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        61.93       61.999       62.008       62.013       62.038        62.05 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       62.069       62.082       62.094       62.155       62.192       62.247 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       62.325       62.351       62.361         62.4       62.485       62.494 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        62.61       62.612       62.649       62.677       62.681       62.698 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       62.728       62.742       62.745        62.82       62.842       62.879 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       62.944       62.974        63.01       63.012        63.03        63.04 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       63.062       63.108     63.11888       63.154       63.179       63.196 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##         63.3       63.306       63.336       63.373       63.441       63.479 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        63.61       63.622       63.625       63.674       63.727       63.728 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       63.739       63.785       63.837        63.87       63.883     63.96736 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       63.983        64.03       64.048       64.062       64.071         64.1 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       64.134       64.151       64.164       64.266       64.274        64.28 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       64.337       64.342        64.36       64.361        64.39       64.399 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       64.406       64.492       64.531        64.59       64.597       64.624 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       64.698        64.75       64.766        64.77        64.79        64.82 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##         64.9        64.93        64.94       64.951       65.032       65.033 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       65.042       65.044       65.142       65.152         65.2       65.205 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       65.246       65.256        65.39       65.393         65.4       65.421 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       65.424       65.483         65.5       65.525       65.528       65.554 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        65.57       65.593        65.61       65.634       65.712       65.742 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        65.77       65.798       65.799       65.815       65.843        65.86 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       65.869         65.9        65.94       65.949       66.041       66.046 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       66.071       66.084       66.099       66.146       66.216        66.22 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       66.234       66.295       66.322       66.353       66.399        66.41 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       66.458        66.55         66.6        66.61       66.653        66.66 
## 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       66.662       66.711       66.798         66.8       66.803        66.87 
## 0.0005868545 0.0005868545 0.0005868545 0.0017605634 0.0005868545 0.0005868545 
##       66.874       66.894        66.91       66.914       66.974       66.983 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       67.044       67.046       67.052       67.057       67.064       67.065 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       67.123        67.13       67.159       67.178       67.217       67.231 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       67.274       67.297       67.298       67.378       67.405        67.41 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        67.45       67.456        67.48        67.49         67.5        67.51 
## 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 
##       67.521        67.64        67.65       67.659        67.66       67.662 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        67.69       67.712       67.727       67.734       67.744       67.768 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        67.81        67.84       67.849        67.85        67.86       67.926 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       67.946        67.96           68       68.015       68.042       68.225 
## 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 
##       68.253        68.29         68.3       68.386       68.421       68.426 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        68.44       68.457       68.468       68.481         68.5        68.54 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       68.557       68.564       68.565       68.588       68.673       68.681 
## 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        68.69         68.7        68.73        68.74        68.75       68.755 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 
##       68.757       68.768       68.832       68.835         68.9        68.93 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 
##       68.976       68.978           69       69.011        69.03       69.052 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##         69.1        69.12        69.15       69.152        69.17        69.18 
## 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 
##        69.21        69.24       69.249        69.26       69.292       69.343 
## 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        69.36       69.388        69.39         69.4       69.451        69.46 
## 0.0005868545 0.0005868545 0.0023474178 0.0005868545 0.0005868545 0.0005868545 
##       69.465       69.481        69.49       69.498         69.5        69.51 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0011737089 
##       69.521        69.53       69.535        69.54        69.58       69.582 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        69.61       69.613       69.615        69.62        69.66        69.69 
## 0.0011737089 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 
##       69.718        69.72       69.745        69.76       69.772       69.806 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        69.81       69.819        69.82        69.83        69.86       69.862 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       69.885         69.9       69.906       69.942        69.95       69.957 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        69.96       69.978           70       70.001        70.11        70.14 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       70.162        70.19       70.198        70.21        70.25       70.259 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        70.26       70.265        70.29         70.3       70.303       70.313 
## 0.0005868545 0.0005868545 0.0011737089 0.0011737089 0.0005868545 0.0005868545 
##        70.32        70.33        70.35       70.379        70.38        70.41 
## 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        70.42       70.426        70.45       70.457        70.46       70.472 
## 0.0017605634 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        70.51       70.533        70.56       70.565        70.59       70.616 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        70.63       70.636        70.64       70.647        70.65        70.67 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       70.672        70.69       70.693        70.71       70.723       70.734 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       70.736        70.75       70.755        70.76       70.774        70.78 
## 0.0005868545 0.0017605634 0.0005868545 0.0011737089 0.0005868545 0.0005868545 
##       70.795         70.8       70.805        70.81       70.815       70.836 
## 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       70.845       70.847        70.85        70.87         70.9        70.93 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        70.94        70.96       70.964        70.97        70.98        70.99 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 
##       70.994           71       71.006       71.028        71.04        71.06 
## 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       71.063        71.08       71.096         71.1        71.14        71.15 
## 0.0005868545 0.0017605634 0.0005868545 0.0011737089 0.0005868545 0.0005868545 
##       71.164        71.19       71.197        71.21       71.218        71.24 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       71.263        71.28         71.3       71.309        71.32       71.322 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 
##       71.338        71.34        71.36        71.38       71.421        71.43 
## 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        71.44       71.455        71.52       71.523       71.527        71.55 
## 0.0011737089 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 
##       71.555        71.58       71.581       71.626        71.63       71.659 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       71.682       71.688       71.752        71.76       71.766        71.77 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       71.777        71.81        71.86       71.868       71.878        71.89 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       71.913       71.918        71.93       71.938       71.954       71.973 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       71.993           72        72.01       72.028        72.03       72.047 
## 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        72.13        72.14       72.146        72.16        72.17       72.178 
## 0.0011737089 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 
##        72.19        72.22       72.232       72.235       72.244        72.25 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       72.262       72.301       72.312        72.34        72.35        72.37 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        72.38        72.39       72.396         72.4       72.462       72.476 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        72.49       72.492       72.499         72.5        72.52       72.527 
## 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       72.535       72.567        72.59       72.601       72.649        72.67 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        72.71       72.737        72.75       72.752        72.76       72.766 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        72.77       72.777         72.8       72.801        72.88       72.889 
## 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       72.899        72.95        72.96       72.961        72.99       73.005 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       73.017       73.042       73.044       73.053        73.06       73.066 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 
##         73.1        73.18       73.213        73.23       73.244       73.275 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       73.338        73.37        73.38         73.4        73.42       73.422 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        73.44        73.45        73.47        73.48        73.49        73.56 
## 0.0011737089 0.0005868545 0.0017605634 0.0005868545 0.0005868545 0.0005868545 
##         73.6       73.615        73.64        73.67        73.68       73.717 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0017605634 0.0005868545 
##        73.73       73.738       73.747        73.75        73.78         73.8 
## 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0011737089 
##        73.82        73.83        73.84       73.911       73.923       73.925 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        73.93       73.952       73.981       74.002        74.01        74.04 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        74.06        74.08        74.09       74.101       74.126       74.143 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        74.16       74.173       74.174       74.193        74.21       74.223 
## 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 
##       74.241       74.249        74.26        74.32        74.34        74.36 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 
##        74.39       74.414        74.45        74.46       74.543        74.55 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        74.63       74.647        74.65       74.663        74.67        74.69 
## 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       74.712        74.72        74.74       74.752       74.772       74.795 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##         74.8        74.83       74.847       74.852        74.86       74.865 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       74.876        74.89       74.902       74.917        74.94        74.98 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       74.994       75.007        75.02        75.13        75.19        75.24 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 
##        75.25       75.307        75.32        75.33        75.35        75.37 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        75.38        75.39       75.435        75.44       75.445        75.45 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       75.467        75.51       75.537       75.563         75.6       75.635 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        75.64       75.651         75.7       75.713       75.744       75.748 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        75.76       75.788       75.816        75.89        75.97        76.04 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 
##        76.05        76.07        76.09        76.11       76.122       76.151 
## 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 
##       76.156       76.195         76.2        76.21         76.3        76.32 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        76.33        76.34       76.384        76.42       76.423       76.442 
## 0.0005868545 0.0005868545 0.0005868545 0.0017605634 0.0005868545 0.0005868545 
##        76.46       76.486        76.66        76.67        76.81        76.83 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        76.86         76.9       76.904        76.93        76.99        77.03 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 
##       77.045        77.11        77.13       77.158        77.18        77.19 
## 0.0005868545 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 
##       77.218        77.23        77.26        77.29        77.31        77.32 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        77.34        77.41        77.42        77.44        77.46        77.51 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        77.53        77.55        77.56        77.57       77.588       77.601 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       77.778       77.783        77.86       77.869       77.926        77.95 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        78.03       78.098       78.123        78.16       78.242       78.256 
## 0.0011737089 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       78.269       78.273        78.32       78.332        78.37         78.4 
## 0.0005868545 0.0005868545 0.0011737089 0.0005868545 0.0005868545 0.0005868545 
##       78.471        78.53       78.553        78.61       78.623        78.64 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        78.67       78.746        78.77       78.782        78.82        78.83 
## 0.0011737089 0.0005868545 0.0017605634 0.0005868545 0.0005868545 0.0005868545 
##       78.885        78.95        78.98        79.05        79.11       79.313 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        79.36        79.37        79.39       79.406       79.425       79.441 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       79.483        79.59       79.696       79.762        79.77        79.78 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       79.829       79.972           80        80.04       80.196       80.204 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##        80.24        80.37         80.5       80.546        80.62       80.653 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       80.657        80.69       80.745       80.884       80.941       81.235 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 
##       81.495       81.701       81.757           82       82.208       82.603 
## 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545 0.0005868545

‘geom_jitter’ kullanımının amacı noktalar birbirinin üstüne binmesin diye oynatır.