Question

in the data set below, what are the lower quartile, the median, and the upper quartile?
1 1 3 3 7 8 9
lower quartile =
median =
upper quartile =

Explanation:

Step1: Order the data (already ordered)

The data set is \(1, 1, 3, 3, 7, 8, 9\).

Step2: Find the median

The number of data points \(n = 7\) (odd). The median is the middle value, at position \(\frac{n + 1}{2}=\frac{7+1}{2}=4\). So the median is the 4th value, which is \(3\).

Step3: Find the lower quartile (Q1)

The lower half of the data is \(1, 1, 3\) (values below the median). The number of values in the lower half is \(3\) (odd). The lower quartile is the middle value of the lower half, at position \(\frac{3 + 1}{2}=2\) in the lower half. So Q1 is the 2nd value of the lower half, which is \(1\).

Step4: Find the upper quartile (Q3)

The upper half of the data is \(7, 8, 9\) (values above the median). The number of values in the upper half is \(3\) (odd). The upper quartile is the middle value of the upper half, at position \(\frac{3 + 1}{2}=2\) in the upper half. So Q3 is the 2nd value of the upper half, which is \(8\).

Answer:

lower quartile = \(1\)
median = \(3\)
upper quartile = \(8\)