Question

Problem 6 (20 points) For the following dataset of 20 values 0 10 25 30 30 50 65 76 100 113 130 130 165 175 179 180 78 185 199 (1) Find its sample mean (2) Find its five-number summary (3) Draw a boxplot for the dataset in the following grid 0 20 40 60 80 100 120 140 160 180 200 (4) Draw a histogram for the dataset in the following grid with 10 bins and decide the bin width and height properly to approximate a probability density function.

Answer 1

w Page solution in n = 20 The data are written in increasing order o 10, 25, 30, 30,5o, 65, 76, 78, 80, 1 100, 113, 130, 130, 165, 175, 179, 180, 185, 199. 1 sample mean = E(X) - Cap = 2000 - min E(X) = 1007 o = max = 1gg first quartile = (xD) sample 5th sample = 30 h sample Kn second quartile = median a loth sample and with CamScane

Third quartie = nyth samele - 15 th sample = 105. fire-number summary is The min min o Q, 30 ma Q2 so Q3 165 max 1gg. Box-piot. +8 7Qz = 165 पि too 80 480 Go Q = 30 Assanned with CamScanner

frequency_height 10 Classes ie. lobins class o-20 20-40 4orbo Go - 80 80 - 100 Ico -120 120 -140 140-160 160-180 180-280 width= 20 - حب - عمم و حیا جا Height = frequency of class width of class N=20 - * width. Height is same as the frequency Histogram. - 2 2 20 40 6o so luo 120 140 160 180 200 canned with CamScanner