Question

in the data set below, what are the lower quartile, the median, and the upper quartile? 19 19 33 33 35 54 62 84 84 lower quartile = median = upper quartile =

Explanation:

Step1: Sort the data (already sorted)

The data set is 19, 19, 33, 33, 35, 54, 62, 84, 84.

Step2: Find the median

There are 9 data - points. The median is the 5th value. So, median = 35.

Step3: Find the lower half

The lower half of the data set is 19, 19, 33, 33.

Step4: Find the lower quartile

Since there are 4 values in the lower half, the lower quartile is the average of the 2nd and 3rd values. $\frac{19 + 33}{2}=26$.

Step5: Find the upper half

The upper half of the data set is 54, 62, 84, 84.

Step6: Find the upper quartile

Since there are 4 values in the upper half, the upper quartile is the average of the 2nd and 3rd values. $\frac{62+84}{2}=73$.

Answer:

lower quartile = 26
median = 35
upper quartile = 73