in the data set below, what are the lower quartile, the median, and the upper quartile? 14 18 19 30 30 33 43…

Explanation:

Step1: Arrange data in order

The data is already in ascending - order: 14, 18, 19, 30, 30, 33, 43, 52, 66, 69, 84.

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 (=33).

Step3: Find the lower half

The lower half of the data is 14, 18, 19, 30, 30. There are (n_1 = 5) data - points. The lower quartile is the (\left(\frac{5 + 1}{2}\right))-th value in the lower half. (\frac{5+1}{2}=3)-rd value. So, lower quartile (=19).

Step4: Find the upper half

The upper half of the data is 43, 52, 66, 69, 84. There are (n_2 = 5) data - points. The upper quartile is the (\left(\frac{5 + 1}{2}\right))-th value in the upper half. (\frac{5+1}{2}=3)-rd value. So, upper quartile (=66).

Answer:

lower quartile = 19 median = 33 upper quartile = 66