in the data set below, what are the lower quartile, the median, and the upper quartile? 16 26 31 31 40 46 64…

Explanation:

Step1: Arrange data and find median

The data set is already in ascending - order: 16, 26, 31, 31, 40, 46, 64, 70, 72, 72, 93. There are (n = 11) data points. The median is the (\left(\frac{n + 1}{2}\right))-th value. So, the median is the (\left(\frac{11+1}{2}\right)=6) - th value, which is 46.

Step2: Find lower half for lower quartile

The lower half of the data set (excluding the median since (n) is odd) is 16, 26, 31, 31, 40. There are (n_1=5) data points. The lower - quartile is the (\left(\frac{5 + 1}{2}\right)=3) - rd value. So, the lower quartile is 31.

Step3: Find upper half for upper quartile

The upper half of the data set (excluding the median since (n) is odd) is 64, 70, 72, 72, 93. There are (n_2 = 5) data points. The upper - quartile is the (\left(\frac{5+1}{2}\right)=3) - rd value. So, the upper quartile is 72.

Answer:

lower quartile = 31 median = 46 upper quartile = 72