Question

in the data set below, what are the lower quartile, the median, and the upper quartile?15 36 40 50 55 61 67 69 74 82lower quartile = median = upper quartile =

Explanation:

Step1: Find the median

The data set has \(n = 10\) values. The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=5\), \(\frac{n}{2}+1 = 6\). The 5th value is \(55\) and the 6th value is \(61\). Median\(=\frac{55 + 61}{2}=\frac{116}{2}=58\).

Step2: Find the lower half and upper half

The lower half of the data set is \(15,36,40,50,55\). The upper half of the data set is \(61,67,69,74,82\).

Step3: Find the lower quartile

For the lower - half (\(n_1=5\) values), the lower quartile (Q1) is the 3rd value. So, \(Q1 = 40\).

Step4: Find the upper quartile

For the upper - half (\(n_2 = 5\) values), the upper quartile (Q3) is the 3rd value. So, \(Q3=69\).

Answer:

lower quartile \(=40\), median \(=58\), upper quartile \(=69\)