Question

2.5.15 (a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 

3 8 8 6 2 9 8 7 9 6 9 5 2 6 29 8 7 79 

(a) Min = _______  (Simplify your answer.)

 2.5.17 (a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data 

3 8 8 4 2 987 969 3 16 29 8 7 79 

(a) Min = _______ 

Answer 1

We know that the five-number summary of the data gives the following thing as below:

Min_value,1st_quartile, Median, 3rd_quartile, Max_Value

2.5.15) Let us assume the data can be written as   X: 3,8,8,6,2,9,8,7,9,6,9,5,2,6,2,9,8,7,7,9

To find the five-number summary, we have to arrange data in ascending order as below:

X1: 2 2 2 3 5 6 6 6 7 7 7 8 8 8 8 9 9 9 9 9, total no. of observation n=20, From the above X1,

Min_value=2, 1st quartile is n/4 i.e. 20/4=5th position number in X1 i.e.5, 3rd quartile is 3n/4 i.e. 3*20/4=15th position number in X1 i.e. 8, Median is n/2 i.e.20/2=10 position number in X1 is 7, Max_value is 9

Hence, five-number summary of X is obtained as, 2,  5, 7, 8, 9. Min_vaue is 2

2.5.17) Let us assume the data can be written as Y: 3,8,8,4,2,9,8,7,9,6,9,3,1,6,2,9,8,7,7,9

To find the five-number summary, we have to arrange data in ascending order as below:

X1: 1,2,2,3,3,4,6,6,7,7,7,8,8,8,8,9,9,9,9,9, total no. of observation n=20, From the above Z1

Min_value=1, 1st quartile is n/4 i.e. 20/4=5th position number in Z1 i.e.3, 3rd quartile is 3n/4 i.e. 3*20/4=15th position number in Z1 i.e. 8, Median is n/2 i.e.20/2=10 position number in Z1 is 7, Max_value is 9

Hence, five-number summary of Z is obtained as, 1, 3, 7, 8, 9. Min_vakue is 1

Box_plot in above two cases is given below: