in the data set below, what are the lower quartile, the median, and the upper quartile? 1 2 3 3 4 5 6 8 8 9…

Explanation:

Step1: Arrange data in order

The data set 1, 2, 3, 3, 4, 5, 6, 8, 8, 9, 9 is already in ascending - order.

Step2: Find the median

There are (n = 11) data points. The median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{11+1}{2}=6)-th value. So, median (= 5).

Step3: Find the lower half

The lower half of the data set is 1, 2, 3, 3, 4. There are (n_1=5) data points. The lower - quartile is the (\left(\frac{5 + 1}{2}\right))-th value, which is the 3 - rd value. So, lower quartile (= 3).

Step4: Find the upper half

The upper half of the data set is 6, 8, 8, 9, 9. There are (n_2 = 5) data points. The upper - quartile is the (\left(\frac{5+1}{2}\right))-th value, which is the 3 - rd value. So, upper quartile (= 8).

Answer:

lower quartile (= 3) median (= 5) upper quartile (= 8)