Question

What is the five number summary for this data set 17,21,26,28,31,33,41,46,52

Answer 1

Given:

The data set is 17, 21, 26, 28, 31, 33, 41, 46, 52.

To find:

The five-number summary for the given data set.

Solution:

We have, the values

17, 21, 26, 28, 31, 33, 41, 46, 52

Divide the data values into 2 equal parts.

(17, 21, 26, 28), 31, (33, 41, 46, 52)

Divide each parenthesis into 2 equal parts.

(17, 21), (26, 28), 31, (33, 41), (46, 52)

Now,

Minimum value = 17

The first quartile is:

$Q_1=\dfrac{21+26}{2}$

$Q_1=\dfrac{47}{2}$

$Q_1=23.5$

Median = 31

The third quartile is:

$Q_3=\dfrac{41+46}{2}$

$Q_3=\dfrac{87}{2}$

$Q_3=43.5$

Maximum value = 52

Therefore, the five-number summary for the given data set is 17, 23.5, 31, 43.5, 52.