in the data set below, what are the lower quartile, the median, and the upper quartile? 3 3 9 8 9 6 lower…

Explanation:

Step1: Sort the data set

First, sort the data set (3,3,6,8,9,9) in ascending - order.

Step2: Find the median

The data set has (n = 6) values. The median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+1))th ordered values. (\frac{n}{2}=3) and (\frac{n}{2}+1 = 4). The 3rd value is (6) and the 4th value is (8), so the median (M=\frac{6 + 8}{2}=7).

Step3: Find the lower half and upper half of the data

The lower - half of the data is (3,3,6) and the upper - half of the data is (8,9,9).

Step4: Find the lower quartile

For the lower - half of the data ((n_1=3) values), the lower quartile (Q_1) is the middle value. So (Q_1 = 3).

Step5: Find the upper quartile

For the upper - half of the data ((n_2 = 3) values), the upper quartile (Q_3) is the middle value. So (Q_3=9).

Answer:

lower quartile = 3 median = 7 upper quartile = 9