Question

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

Explanation:

Step1: Sort the data

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

Step2: Find the median

The median is the middle value of a sorted data set. Since there are \(n = 10\) data points, the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th values. \(\frac{10}{2}=5\), \(\frac{10}{2}+1 = 6\). The 5th value is \(7\) and the 6th value is \(9\). Median \(M=\frac{7 + 9}{2}=8\)

Step3: Find the lower quartile

The lower half of the data is \(4,4,6,7,7\). Since there are \(n = 5\) data points in the lower half, the lower quartile \(Q_1\) is the 3rd value. So \(Q_1=6\)

Step4: Find the upper quartile

The upper half of the data is \(9,9,9,9,9\). Since there are \(n = 5\) data points in the upper half, the upper quartile \(Q_3\) is the 3rd value. So \(Q_3=9\)

Answer:

lower quartile \(=6\)
median \(=8\)
upper quartile \(=9\)