Question

Please draw boxplot

38) [6 points] The test scores of 30 students are listed below. Find the five-number summary and then draw a boxplot that represents the data. 31 41 45 48 52 55 56 56 63 65 67 67 69 70 70 74 75 78 79 79ue Ti (al 80 81 83 85 85 87 90 92 95 99 o2:M Q3: Minimum value: Q1: Maximum value: 49 TOBO 40 100 iD 30 4D

Answer 1

To get the quartiles first sort the data in ascending order 52 70 85 65 45 69 83 48 56 56 63 67 80 67 85 87 90 92 95 When number of observations n is even (n 30), then median (2nd quartile) is th obs (30 03015h 3657074-72 2 2 2 The first quartile, is the median of the lower half of the data set. This means that about 25% of the numbers in the data set lie below Q1 and about 75% lie above Q1 31 67 80 48 70 85 56 56 63 65 67 81 69 83 70 85 74 87 78 90 95 th obs ie. 15 observations, the median for odd numbered n ) n+1 Lower half of the data i.e. 15 observations, the median for odd numbered n 一 = 8th observation is at the middle (7 observations to the left and 7 observations to the right) Hence Q1 56 Similarly, the third quartile, is the median of the upper half of the data set. This means that about 75% of the numbers in the data set lie below Q3 and about 25% lie above Q3 67 80 67 81 69 83 48 70 85 52 70 85 74 87 56 75 90 56 78 92 63 79 95 65 79 Minimum- 31 and maximum-99 To draw a boxplot we have five point summary Minimum, 1st quartile, 2nd quartile (median), 3rd quartile, maximum. The five point summary is 31,56,72, 83,99 The boxplot would be a line from the smallest value to the largest value and drawing a box from Q1 to Qs with a line in the middle for the median, e.g boxplot would look like as below

30 40 50 60 70 80 90 100 110