Question

in the data set below, what are the lower quartile, the median, and the upper quartile? 8 5 9 6 4 6 7 lower quartile = median = upper quartile =

Explanation:

Step1: Sort the data set

Sort the data set \(8,5,9,6,4,6,7\) in ascending order: \(4,5,6,6,7,8,9\).

Step2: Find the median

The median is the middle value. Since there are \(n = 7\) values, the median is the \(\frac{n + 1}{2}=\frac{7+1}{2}=4\)th value. So the median is \(6\).

Step3: Find the lower quartile

The lower half of the data is \(4,5,6\). The lower quartile is the middle value of the lower half. Since there are \(3\) values, the lower quartile is the \(\frac{3 + 1}{2}=2\)nd value, which is \(5\).

Step4: Find the upper quartile

The upper half of the data is \(7,8,9\). The upper quartile is the middle value of the upper half. Since there are \(3\) values, the upper quartile is the \(\frac{3+1}{2}=2\)nd value, which is \(8\).

Answer:

lower quartile \(=5\), median \(=6\), upper quartile \(=8\)