Question

in the data set below, what are the lower quartile, the median, and the upper quartile? 8 2 1 1 2 4 3 lower quartile = median = upper quartile =

Explanation:

Step1: Sort the data

Sort the data set \(8, 2, 1, 1, 2, 4, 3\) in ascending order: \(1, 1, 2, 2, 3, 4, 8\).

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 the median is \(2\).

Step3: Find the lower quartile

The lower half of the data is \(1, 1, 2\). The lower quartile \(Q_1\) is the middle value of the lower half. Since there are \(3\) values, \(Q_1\) is the \(\frac{3 + 1}{2}=2\) -nd value. So \(Q_1 = 1\).

Step4: Find the upper quartile

The upper half of the data is \(3, 4, 8\). The upper quartile \(Q_3\) is the middle value of the upper half. Since there are \(3\) values, \(Q_3\) is the \(\frac{3+1}{2}=2\) -nd value. So \(Q_3 = 4\).

Answer:

lower quartile \(=1\), median \(=2\), upper quartile \(=4\)