Section 2.1

  1. A frequency distribution lists the number of occurences of each catagory of data, while a relative fequency distribution lists the proportion of occurences of each catagory of data.

3 The relative frequencies should add up to 1.

  1. The most common approach is washing your hands. 61% of the population chooses this method.

  2. Drinking oragne juice is the least used approach. Only 2% of the population chooses this method.

  3. 25% of the population believed getting a flu shot is the best way to prevent getting the flu.

datt <- c(125, 324, 552, 1257, 2518)

rel.freqq <- datt/sum(datt)

categoriess <- c("Never", "Rarely", "Sometimes", "Most of time", "Always")


answerr <- data.frame(categoriess,rel.freqq)

answerr
##    categoriess  rel.freqq
## 1        Never 0.02617253
## 2       Rarely 0.06783920
## 3    Sometimes 0.11557789
## 4 Most of time 0.26319095
## 5       Always 0.52721943

  1. 53% of students answered “Always”

  2. 3% answered “Never,” while 7# answered “Rarely”

barplot(datt,main="Seat Belt Usage",names=categoriess, col =c("red","blue","green","yellow","orange"))

barplot(rel.freqq,main="Seat Belt Usage",names=categoriess, col =c("red","blue","green","yellow","orange"))

pie(datt,main="Seat Belt Usage",labels=categoriess, col =c("red","blue","green","yellow","orange"))

  1. This is an inferential statement, because it is a conclusion based on data.
dat <- c(377,192,132,81,243)

rel.freq <- dat/sum(dat)

categories <- c("More 1", "Up to 1", "Few a week", "Few a month", "Never")


answer <- data.frame(categories,rel.freq)

answer
##    categories   rel.freq
## 1      More 1 0.36780488
## 2     Up to 1 0.18731707
## 3  Few a week 0.12878049
## 4 Few a month 0.07902439
## 5       Never 0.23707317

  1. 23.7% of the people never uses the internet

barplot(dat,main="Internet Usage",names=categories, col =c("red","blue","green","yellow","orange"))

barplot(rel.freq,main="Internet Usage(Relative Freq)",names=categories, col =c("red","blue","green","yellow","orange"))

pie(dat,main="Internet Usage",labels=categories, col =c("red","blue","green","yellow","orange"))

Section 2.2

  1. False, t is right skewed.

  2. False, it is bell-shaped.

9

  1. The most frequent outcome of the dice is 8.

  2. The least frequent outcome is 2.

  3. A 7 was observed 15 times.

  4. 4 more 5’s were observed than 4’s.

  5. A 7 was observed 15% od the time.

  6. The shape of distribution is left-skewed.

10

  1. 4 is the most frequent amount of cars sold in a week.

  2. Two cars were sold for 9 weeks.

  3. Two cars were sold 17% of the time.

  4. The shape of distribution is right-skewed.

13

  1. Skewed right, because there are more lower to middle-class households than there are upper-class.

  2. Bell-shaped, because there are more people in the average for standardized tests.

  3. Skewed right, because most households have 5 or less people in them.

  4. Skewed left, because most Alzheimer’s patients are of old age.

14

  1. Skewed right, because most people have few drinks during the week.

  2. Uniform, because the ages range.

  3. Skewed left, because most people who need hearing aid are of old age.

  4. Skewed left, because men tend to be above 5’5.

15

dattt <- c(16, 18, 12, 3, 1)

rel.freqqq <- dattt/sum(dattt)

categoriesss <- c("Zero", "One", "Two", "Three", "Four")

answerrr <- data.frame(categoriesss,rel.freqqq)

answerrr
##   categoriesss rel.freqqq
## 1         Zero       0.32
## 2          One       0.36
## 3          Two       0.24
## 4        Three       0.06
## 5         Four       0.02

  1. 24% of housegoles have two children under the age of five.

  2. 60% of households have one or two children under the age of five.

16

free_throws <- c(16, 11, 9, 7, 2,3,0,1,0,1)

rel.freqqq <- free_throws/sum(free_throws)

categoriesss <- c("1", "2", "3", "4","5","6","7","8","9","10")

answerrr <- data.frame(categoriesss,rel.freqqq)

answerrr
##    categoriesss rel.freqqq
## 1             1       0.32
## 2             2       0.22
## 3             3       0.18
## 4             4       0.14
## 5             5       0.04
## 6             6       0.06
## 7             7       0.00
## 8             8       0.02
## 9             9       0.00
## 10           10       0.02

  1. She missed on the fourth free throw 18% of the time.

  2. She missed on the tenth free throw 0% of the time.

  3. She at least made five free throws 4% of the time.

25

  1. This data is discrete.

tv <- c(1, 1, 1, 2, 1,
        1, 2, 2, 3, 2,
        4, 2, 2, 2, 2,
        2, 4, 1, 2, 2,
        3, 1, 3, 1, 2,
        3, 1, 1, 2, 1,
        5, 0 ,1, 3, 3,
        1, 3, 3, 2, 1)

#table(tv)

tv <- c(1,14,14,8,2,1)

tv.freq <- tv/sum(tv)

tv.cat <- c("0", "1", "2", "3","4","5")

freq.tab <- data.frame(tv.cat,tv)
rfreq.tab <- data.frame(tv.cat,tv.freq)


freq.tab
##   tv.cat tv
## 1      0  1
## 2      1 14
## 3      2 14
## 4      3  8
## 5      4  2
## 6      5  1
rfreq.tab
##   tv.cat tv.freq
## 1      0   0.025
## 2      1   0.350
## 3      2   0.350
## 4      3   0.200
## 5      4   0.050
## 6      5   0.025

  1. 20% of households have three TVs.

  2. 7.5% of households have four or more TVs.