Question

the number of points Josh were scored during the last eight basketball games are listed below what are the lower, middle, and upper quartile values of the numbers of points?

Answer 1

C. lower: 6

middle: 13

upper: 17

Step-by-step explanation

First we have to order this data from lowest to highest value:

`5,6,6,12,14,17,17,24`

The middle quartyle is the median of the data set. Since this set has 8 values, which is even, the median is the mean of the two middle values: 12 and 14:

`Q_{\text{middle}}=(12+14)/(2)=(26)/(2)=13`

Then, the lower quartile is the median of the first half of the data set. Since the median of the whole data set is located between 12 and 14, the first half of the set is:

`5,6,6,12`

This is too an even number of values, but since the two middle values are the same the lower quartile is that value: 6.

Then, the upper quartile is the median of the second half of the data set:

`14,17,17,24`

For this quartile is the same as the lower quartile, the number of values is even and the two middle values are the same. The upper quartile is 17