Question

What is the five-number summary for this data set?

12, 15, 17, 20, 22, 25, 27, 30, 33, 37
Assume the numbers in each answer choice are listed in this order: min, Q1,
median, Q3, max.

Answer 1

Answer: min = 12, Q1 =17, median =23.5 , Q3 = 30, max = 37 .

Explanation:

The five-number summary for this data set consists of min, Q1,

median, Q3, max.

Given data: 12, 15, 17, 20, 22, 25, 27, 30, 33, 37, which is already arranged in a order.

Minimum value = 12

Maximum value = 37

since , number of observations = 10 (even)

So , Median = Mean of middle most terms

Middle most terms = 22, 25

Median =
`(22+25)/(2)=23.5`

First quartile (
`Q_1`)= Median of first half ( 12, 15, 17, 20, 22)

= middle most term

= 17

Third quartile (
`Q_3`) = Median of second half (25, 27, 30, 33, 37)

= middle most term

= 30

Hence, five-number summary for this data set :

min = 12, Q1 =17, median =23.5 , Q3 = 30, max = 37 .