Question

in the data set below, what are the lower quartile, the median, and the upper quartile? 1 1 1 2 2 4 4 5 6 7 lower quartile = median = upper quartile =

Explanation:

Step1: Arrange the data

The data set is already in ascending order: \(1,1,1,2,2,4,4,5,6,7\).

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 5th value is \(2\) and the 6th value is \(4\). Median \(=\frac{2 + 4}{2}=3\).

Step3: Find the lower quartile

The lower half of the data is \(1,1,1,2,2\). There are \(n_1=5\) data points. The lower quartile is the 3rd value. Lower quartile \(=1\).

Step4: Find the upper quartile

The upper half of the data is \(4,5,6,7\). There are \(n_2 = 5\) data points. The upper quartile is the 3rd value of the upper - half. Upper quartile \(=5\).

Answer:

lower quartile \(=1\)
median \(=3\)
upper quartile \(=5\)