Question

2. Find the five-number summary and construct a boxplot for the following data: 12, 31, 23, 8, 23, 11, 33, 17, 28, 23, 23, 16

Answer 1

Solution and We have to find the five-number Summary Construct a boxplot for the following data 12,31, 23,8, 23,1, 33,17, 28, 23,23,16 a data set Value in 8 data set is n=12 Now to arrange the given data in ascending onder 8,10,12,16,17, 23, 23,23, 23, 28, 31,33 Hare Minimum is the smallest Therefore the minimum * Now to find the first Quartile , Q, :- the bottom half of The first is the median of Quartile the numbers. So the bottom half is value of the 8, 12, 16,17,23 The median of these numbers is 14 Therefore the first quartile of the data set is [14 * Now to find the Second Quasitile (Q2) The second Quartile (Qc) is the middle number in a santed list of numbers. ondering the data from least to greatest, we get 8,11,12,16,17,23,23,23,23, 28, 31, 33

Therefore 23+23 Median 46 23 23 Median Hence the Second Quantike is * Now to find the third Quartile (Q3) : The third Quarble is the median of the upper half of the numbers. So the upper half is 93,23,23,28,31,33 25.5 Therefore the median of these numbers is Hence the third quartile of the data set is (25.5 * Now to find Maximum value set 33 The maximum is the greatest Value in data Therefore the maximum value of the data set is

draw the box Plot 3 for the given" data Now to Maximum Value = 33 Third Quartile 25.5 Median First Quartile = 14 Minimum Value = 8