Question

A random sample of 45 people was asked to record the number of kilometres travelled by a
minibus in a given week. The distances, to the nearest kilometre, are shown below:
32 37 52 42 42 42 40 61 48 45
49 32 49 44 44 49 44 33 37 32
33 36 32 39 46 45 41 22 39 39
43 40 40 49 42 36 51 44 43 46
(i) Construct a grouped frequency distribution using the classes 22 – 26, 27 – 31, …
(ii) Construct a frequency histogram.
(iii)Construct a frequency polygon.
(iv) Describe the shape of the distribution.

Answer 1

part iv) the shape of the distribution is mesokurtic(symmetric) in nature.

> # part i) grouped frequency distribution 1> data <- c(32,37,52,42,42,42,40,61,48,45,49,32,49,44,44,49,44,33, 37,32,33,36,32,39,46,45,41,22,39,39,43,40,40,49,42,36,51,44,43,46) > range (data) [1] 22 61 > breaks <- seg(22,62,4) 1> data.cut <- cut(data, breaks, right = FALSE) > data. freq <- table (data.cut) > freg_distribution <- data.frame (data.freq) > freq_distribution data.cut Freg 1 [22,26) 1 [26, 30) 0 13 130,34) 6 [34,38) 5 [38, 42) 6 [42,46) 7 [46,50) [50,54) S2 9 [54,58) 0 10 [58,62) 1 > # part ii) frequency histogram > f <- c(freq_distribution $Freq):f [1] 1 0 6 4 7 12 7 2 0 1 > lb <- seq(22,58,4); ub <- seq (26,62,4) > X <- (7b+ub)/2 > y <- rep (x, f);b=c(lb, > hist(y, breaks = b,col = "pink", main = "frequency histogram") > # part iii) fregency polygon > plot (x,f,"l",main = "frequency ploygon") > # the shape of the distribution is mes okurtic(symmetric) in natu OOOOUAWNH ге.

Frequency 246,810 12 30 frequency histogram OS 09

4 6 8 10 12 frequency ploygon 50