Question

in the data set below, what are the lower quartile, the me
4 1 2 2 5 2 2 5 4 4
lower quartile =
median =
upper quartile =

Explanation:

Step1: Sort the data

Sort the data set \(4,1,2,2,5,2,2,5,4,4\) in ascending order: \(1,2,2,2,2,4,4,4,5,5\)

Step2: Find the median

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. \(\frac{n}{2}=5\), \(\frac{n}{2}+1 = 6\). The \(5\)th value is \(2\) and the \(6\)th value is \(4\). Median \(=\frac{2 + 4}{2}=3\)

Step3: Find the lower quartile

The lower half of the data is \(1,2,2,2,2\). Since there are \(n_1=5\) data points. The lower quartile is the \(\frac{n_1 + 1}{2}\)th value. \(\frac{5+1}{2}=3\)rd value. Lower quartile \(=2\)

Step4: Find the upper quartile

The upper half of the data is \(4,4,4,5,5\). Since there are \(n_2 = 5\) data points. The upper quartile is the \(\frac{n_2+1}{2}\)th value. \(\frac{5 + 1}{2}=3\)rd value. Upper quartile \(=4\)

Answer:

lower quartile \(=2\)
median \(=3\)
upper quartile \(=4\)