Question

What is the five number summary for this data set?

3, 8, 14, 19, 22, 29, 33, 37, 43, 49
Assume the numbers in each answer choice are listed in this order: min, Q1,
median, Q3, max

Answer 1

see explanation

Explanation:

The median is the middle value of the data set in ascending order. If there is no exact middle then the median is the average of the values either side of the middle.

Given

3 8 14 19 22 29 33 37 43 49

↑ middle is between 22 and 29

median =
`(22+29)/(2)` =
`(51)/(2)` = 25.5

The upper quartile
`Q_(3)` is the middle value of the data to the right of the median.

29 33 37 43 49

↑

`Q_(3)` = 37

The lower quartile
`Q_(1)` is the middle value of the data to the left of the median.

3 8 14 19 22

↑

`Q_(1)` = 14

The min is the smallest value in the data set, that is 3

The max is the largest value in the data set, that is 49

The 5 number summary is

3, 14, 25.5, 37, 49