Question

in the data set below, what are the lower quartile, the median, and the upper quartile? 72 87 72 83 61 73 36 55 68 24 71 lower quartile = median = upper quartile =

Explanation:

Step1: Sort the data

Sort the data set \(24,36,55,61,68,71,72,72,73,87\).

Step2: Find the median

There are \(n = 10\) data points. 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 \(5\)th value is \(68\), the \(6\)th value is \(71\). Median\(=\frac{68 + 71}{2}=69.5\).

Step3: Find the lower quartile

The lower half of the data is \(24,36,55,61,68\). There are \(n_1=5\) data points. The lower quartile is the \(\frac{n_1 + 1}{2}\)th value. \(\frac{n_1+1}{2}=3\)rd value. Lower quartile\( = 55\).

Step4: Find the upper quartile

The upper half of the data is \(71,72,72,73,87\). There are \(n_2 = 5\) data points. The upper quartile is the \(\frac{n_2+1}{2}\)th value. \(\frac{n_2 + 1}{2}=3\)rd value. Upper quartile\(=72\).

Answer:

lower quartile \(=55\), median \(=69.5\), upper quartile \(=72\)