R - Mean, Median, Mode
MOHAMMAD SHADAN
January 16, 2017
Measures of Central Tendency
- Mean : Average
- Median : Middle Value
- Mode : Most Often
x <- c(8,2,7,1,2,9,8,2,10,9)
#Exploratory Data Analysis
hist(x)
boxplot(x)
Mean : The mean is the average of the numbers
sum(x)/length(x)## [1] 5.8#?mean
#Function in base R
mean(x)## [1] 5.8Median : the middle number given the numbers are in order (sorted)
sort(x)## [1] 1 2 2 2 7 8 8 9 9 10#?median
median(x)## [1] 7.5Mode : The number which appears most often in a set of numbers
#There is no function in base R to find mode of set of numbers
x <- c(8,2,7,1,2,9,8,2,10,9)
#Function to find Mode
x## [1] 8 2 7 1 2 9 8 2 10 9#?table
y <- table(x)
y## x
## 1 2 7 8 9 10
## 1 3 1 2 2 1names(y)[which(y==max(y))]## [1] "2"#or in single line
names(table(x))[table(x)==max(table(x))]## [1] "2"#Testing if there are two or more numbers with same frequncy
x <- c(8,2,7,1,2,9,8,2,10,9,8)
sort(x)## [1] 1 2 2 2 7 8 8 8 9 9 10#Mode
names(table(x))[table(x)==max(table(x))]## [1] "2" "8"Mean, Median and Mode using mtcars dataset
head(mtcars)## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1x <- mtcars$wtMean
mean(x)## [1] 3.21725Median
median(x)## [1] 3.325Mode
y <- table(x)
y## x
## 1.513 1.615 1.835 1.935 2.14 2.2 2.32 2.465 2.62 2.77 2.78 2.875
## 1 1 1 1 1 1 1 1 1 1 1 1
## 3.15 3.17 3.19 3.215 3.435 3.44 3.46 3.52 3.57 3.73 3.78 3.84
## 1 1 1 1 1 3 1 1 2 1 1 1
## 3.845 4.07 5.25 5.345 5.424
## 1 1 1 1 1names(y)[which(y==max(y))]## [1] "3.44"#or
names(table(x))[table(x)==max(table(x))]## [1] "3.44"Mean, Median and Mode using airquality dataset
I am using airquality dataset because it has missing values
#Summary Statistics
dim(airquality)## [1] 153 6names(airquality)## [1] "Ozone" "Solar.R" "Wind" "Temp" "Month" "Day"str(airquality)## 'data.frame': 153 obs. of 6 variables:
## $ Ozone : int 41 36 12 18 NA 28 23 19 8 NA ...
## $ Solar.R: int 190 118 149 313 NA NA 299 99 19 194 ...
## $ Wind : num 7.4 8 12.6 11.5 14.3 14.9 8.6 13.8 20.1 8.6 ...
## $ Temp : int 67 72 74 62 56 66 65 59 61 69 ...
## $ Month : int 5 5 5 5 5 5 5 5 5 5 ...
## $ Day : int 1 2 3 4 5 6 7 8 9 10 ...head(airquality)## Ozone Solar.R Wind Temp Month Day
## 1 41 190 7.4 67 5 1
## 2 36 118 8.0 72 5 2
## 3 12 149 12.6 74 5 3
## 4 18 313 11.5 62 5 4
## 5 NA NA 14.3 56 5 5
## 6 28 NA 14.9 66 5 6#Column names with missing Values
names(airquality)[colSums(is.na(airquality)) > 0]## [1] "Ozone" "Solar.R"airquality$Ozone## [1] 41 36 12 18 NA 28 23 19 8 NA 7 16 11 14 18 14 34
## [18] 6 30 11 1 11 4 32 NA NA NA 23 45 115 37 NA NA NA
## [35] NA NA NA 29 NA 71 39 NA NA 23 NA NA 21 37 20 12 13
## [52] NA NA NA NA NA NA NA NA NA NA 135 49 32 NA 64 40 77
## [69] 97 97 85 NA 10 27 NA 7 48 35 61 79 63 16 NA NA 80
## [86] 108 20 52 82 50 64 59 39 9 16 78 35 66 122 89 110 NA
## [103] NA 44 28 65 NA 22 59 23 31 44 21 9 NA 45 168 73 NA
## [120] 76 118 84 85 96 78 73 91 47 32 20 23 21 24 44 21 28
## [137] 9 13 46 18 13 24 16 13 23 36 7 14 30 NA 14 18 20airquality$Solar.R## [1] 190 118 149 313 NA NA 299 99 19 194 NA 256 290 274 65 334 307
## [18] 78 322 44 8 320 25 92 66 266 NA 13 252 223 279 286 287 242
## [35] 186 220 264 127 273 291 323 259 250 148 332 322 191 284 37 120 137
## [52] 150 59 91 250 135 127 47 98 31 138 269 248 236 101 175 314 276
## [69] 267 272 175 139 264 175 291 48 260 274 285 187 220 7 258 295 294
## [86] 223 81 82 213 275 253 254 83 24 77 NA NA NA 255 229 207 222
## [103] 137 192 273 157 64 71 51 115 244 190 259 36 255 212 238 215 153
## [120] 203 225 237 188 167 197 183 189 95 92 252 220 230 259 236 259 238
## [137] 24 112 237 224 27 238 201 238 14 139 49 20 193 145 191 131 223x <- airquality$Solar.R
table(is.na(x))##
## FALSE TRUE
## 146 7x## [1] 190 118 149 313 NA NA 299 99 19 194 NA 256 290 274 65 334 307
## [18] 78 322 44 8 320 25 92 66 266 NA 13 252 223 279 286 287 242
## [35] 186 220 264 127 273 291 323 259 250 148 332 322 191 284 37 120 137
## [52] 150 59 91 250 135 127 47 98 31 138 269 248 236 101 175 314 276
## [69] 267 272 175 139 264 175 291 48 260 274 285 187 220 7 258 295 294
## [86] 223 81 82 213 275 253 254 83 24 77 NA NA NA 255 229 207 222
## [103] 137 192 273 157 64 71 51 115 244 190 259 36 255 212 238 215 153
## [120] 203 225 237 188 167 197 183 189 95 92 252 220 230 259 236 259 238
## [137] 24 112 237 224 27 238 201 238 14 139 49 20 193 145 191 131 223Mean
mean(x)## [1] NA# ?mean
mean(x, na.rm = TRUE)## [1] 185.9315Median
median(x)## [1] NAmedian(x, na.rm = TRUE)## [1] 205Mode
We will not have issue of removing NA for finding Mode
sort(table(x))## x
## 7 8 13 14 19 20 25 27 31 36 37 44 47 48 49 51 59 64
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 65 66 71 77 78 81 82 83 91 95 98 99 101 112 115 118 120 131
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 135 138 145 148 149 150 153 157 167 183 186 187 188 189 192 193 194 197
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 201 203 207 212 213 215 222 224 225 229 230 242 244 248 253 254 256 258
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 260 266 267 269 272 275 276 279 284 285 286 287 290 294 295 299 307 313
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 314 320 323 332 334 24 92 127 137 139 190 191 236 237 250 252 255 264
## 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2
## 273 274 291 322 175 220 223 238 259
## 2 2 2 2 3 3 3 4 4names(table(x))[table(x)==max(table(x))] #x<- airquality$Solar.R## [1] "238" "259"# sort(table(x))
# sort(table(x, useNA = "always"))Summary fuctions
- summary() #Base R
- describe() #Package
psych
summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000summary(airquality)## Ozone Solar.R Wind Temp
## Min. : 1.00 Min. : 7.0 Min. : 1.700 Min. :56.00
## 1st Qu.: 18.00 1st Qu.:115.8 1st Qu.: 7.400 1st Qu.:72.00
## Median : 31.50 Median :205.0 Median : 9.700 Median :79.00
## Mean : 42.13 Mean :185.9 Mean : 9.958 Mean :77.88
## 3rd Qu.: 63.25 3rd Qu.:258.8 3rd Qu.:11.500 3rd Qu.:85.00
## Max. :168.00 Max. :334.0 Max. :20.700 Max. :97.00
## NA's :37 NA's :7
## Month Day
## Min. :5.000 Min. : 1.0
## 1st Qu.:6.000 1st Qu.: 8.0
## Median :7.000 Median :16.0
## Mean :6.993 Mean :15.8
## 3rd Qu.:8.000 3rd Qu.:23.0
## Max. :9.000 Max. :31.0
## #install.packages("psych")
library(psych)
describe(mtcars)## vars n mean sd median trimmed mad min max range skew
## mpg 1 32 20.09 6.03 19.20 19.70 5.41 10.40 33.90 23.50 0.61
## cyl 2 32 6.19 1.79 6.00 6.23 2.97 4.00 8.00 4.00 -0.17
## disp 3 32 230.72 123.94 196.30 222.52 140.48 71.10 472.00 400.90 0.38
## hp 4 32 146.69 68.56 123.00 141.19 77.10 52.00 335.00 283.00 0.73
## drat 5 32 3.60 0.53 3.70 3.58 0.70 2.76 4.93 2.17 0.27
## wt 6 32 3.22 0.98 3.33 3.15 0.77 1.51 5.42 3.91 0.42
## qsec 7 32 17.85 1.79 17.71 17.83 1.42 14.50 22.90 8.40 0.37
## vs 8 32 0.44 0.50 0.00 0.42 0.00 0.00 1.00 1.00 0.24
## am 9 32 0.41 0.50 0.00 0.38 0.00 0.00 1.00 1.00 0.36
## gear 10 32 3.69 0.74 4.00 3.62 1.48 3.00 5.00 2.00 0.53
## carb 11 32 2.81 1.62 2.00 2.65 1.48 1.00 8.00 7.00 1.05
## kurtosis se
## mpg -0.37 1.07
## cyl -1.76 0.32
## disp -1.21 21.91
## hp -0.14 12.12
## drat -0.71 0.09
## wt -0.02 0.17
## qsec 0.34 0.32
## vs -2.00 0.09
## am -1.92 0.09
## gear -1.07 0.13
## carb 1.26 0.29describe(airquality)## vars n mean sd median trimmed mad min max range skew
## Ozone 1 116 42.13 32.99 31.5 37.80 25.95 1.0 168.0 167 1.21
## Solar.R 2 146 185.93 90.06 205.0 190.34 98.59 7.0 334.0 327 -0.42
## Wind 3 153 9.96 3.52 9.7 9.87 3.41 1.7 20.7 19 0.34
## Temp 4 153 77.88 9.47 79.0 78.28 8.90 56.0 97.0 41 -0.37
## Month 5 153 6.99 1.42 7.0 6.99 1.48 5.0 9.0 4 0.00
## Day 6 153 15.80 8.86 16.0 15.80 11.86 1.0 31.0 30 0.00
## kurtosis se
## Ozone 1.11 3.06
## Solar.R -1.00 7.45
## Wind 0.03 0.28
## Temp -0.46 0.77
## Month -1.32 0.11
## Day -1.22 0.72Summary
#Mean
mean(x)## [1] NA#Median
median(x)## [1] NA#Mode
names(table(x))[table(x)==max(table(x))]## [1] "238" "259"