Question

The stemplot below displays the times, in seconds, for 25 students to run 100 meters.

A stemplot titled 100 meter times (seconds) has values 22, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 26, 27, 27, 27, 28, 28, 28, 28, 29, 29, 30.

Which of the following is the correct five-number summary?

22, 24, 26, 28, 29
23, 24.5, 26, 28, 29
22, 24, 27, 28, 30
22, 24.5, 26, 28, 30

Answer 1

Given:

The data values are 22, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 26, 27, 27, 27, 28, 28, 28, 28, 29, 29, 30.

To find:

The five-number summary.

Solution:

We have,

22, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 26, 27, 27, 27, 28, 28, 28, 28, 29, 29, 30

Divide the data values on 2 equal parts.

(22, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26), 26, (26, 26, 27, 27, 27, 28, 28, 28, 28, 29, 29, 30)

Divide each parentheses in two equal parts.

(22, 23, 23, 24, 24, 24), (25, 25, 25, 25, 26, 26), 26, (26, 26, 27, 27, 27, 28), (28, 28, 28, 29, 29, 30)

Now,

Minimum value = 22

`Q_1=(24+25)/(2)=24.5`

Median = 26

`Q_2=(28+28)/(2)=28`

Maximum value = 30

So, the five number summary is 22, 24.5, 26, 28, 30.

Therefore, the correct option is D.