Question

The accompanying frequency table shows the heights? (in inches) of 130 members of a choir. a right parenthesis Find the median and IQR. b right parenthesis Find the sample mean and sample standard deviation. c right parenthesis Display these data with a histogram. d right parenthesis Write a few sentences describing the distribution of heights. frequency table of heights of choir members. ?

Height Count

60 1

61 6

62 10

63 6

64 3

65 20

66 19

67 9

68 13

69 5

70 9

71 8

72 10

73 5

74 1

75 4

76 1

Answer 1

height = 60:76
count = c(1,6,10,6,3,20,19,9,13,5,9,8,10,5,1,4,1)
d = cbind(height,count)
d=as.data.frame(d)
d2= <- rep(d$height, d$count)
multi.fun <- function(x) {
c(mean = mean(x), median = median(x), sd = sd(x),IQR = IQR(x))
}

multi.fun(d2)

mean median sd IQR
67.192308 66.500000 3.725246 5.000000

a) median = 66.5000 and Interquartile range = Q3-Q1 = 5.000

b) sample mean = 67.192308 sample standard deviation = 3.725246

c)

see the attachement

d) The curve look like normal approximately at maximum value that mode at the 65 near to mean = 67.192308 and median = 66.500