Question

in the data set below, what are the lower qu
1 2 4 6 6 7 8
lower quartile =
median =
upper quartile =

Explanation:

Step1: Arrange the data in ascending order

The data set is already in ascending order: \(1, 2, 4, 6, 6, 7, 8\)

Step2: Find the median

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

Step3: Find the lower quartile

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

Step4: Find the upper quartile

The upper half of the data is \(6, 7, 8\). The upper quartile is the middle value of the upper half. Since there are \(3\) values, the upper quartile is the \(\frac{3 + 1}{2}\)th value. \(\frac{3+1}{2}=2\)nd value. So, upper quartile \(=7\)

Answer:

lower quartile \(=2\), median \(=6\), upper quartile \(=7\)