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}](https://tex.z-dn.net/?f=Q_1%3D%5Cdfrac%7B21%2B26%7D%7B2%7D)
![Q_1=\dfrac{47}{2}](https://tex.z-dn.net/?f=Q_1%3D%5Cdfrac%7B47%7D%7B2%7D)
![Q_1=23.5](https://tex.z-dn.net/?f=Q_1%3D23.5)
Median = 31
The third quartile is:
![Q_3=\dfrac{41+46}{2}](https://tex.z-dn.net/?f=Q_3%3D%5Cdfrac%7B41%2B46%7D%7B2%7D)
![Q_3=\dfrac{87}{2}](https://tex.z-dn.net/?f=Q_3%3D%5Cdfrac%7B87%7D%7B2%7D)
![Q_3=43.5](https://tex.z-dn.net/?f=Q_3%3D43.5)
Maximum value = 52
Therefore, the five-number summary for the given data set is 17, 23.5, 31, 43.5, 52.