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:
[tex]Q_1=\dfrac{21+26}{2}[/tex]
[tex]Q_1=\dfrac{47}{2}[/tex]
[tex]Q_1=23.5[/tex]
Median = 31
The third quartile is:
[tex]Q_3=\dfrac{41+46}{2}[/tex]
[tex]Q_3=\dfrac{87}{2}[/tex]
[tex]Q_3=43.5[/tex]
Maximum value = 52
Therefore, the five-number summary for the given data set is 17, 23.5, 31, 43.5, 52.
