in the data set below, what are the lower quartile, the median, and the upper quartile? 14 40 62 27 14 54 14…

Explanation:

Step1: Sort the data set

Arrange the data set (14,40,62,27,14,54,14) in ascending - order: (14,14,14,27,40,54,62).

Step2: Find the median

The data set has (n = 7) values. The median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{7+1}{2}=4)-th value. So the median is (27).

Step3: Find the lower half

The lower half of the data set is (14,14,14). The median of the lower half is the lower - quartile. Since there are (3) values, the median of this lower half (the lower - quartile) is (14).

Step4: Find the upper half

The upper half of the data set is (40,54,62). The median of the upper half is the upper - quartile. Since there are (3) values, the median of this upper half (the upper - quartile) is (54).

Answer:

lower quartile = (14) median = (27) upper quartile = (54)