Question

in the data set below, what are the lower quartile, the median, and the upper quartile?
3 3 3 5 6 9 9
lower quartile =
median =
upper quartile =

Explanation:

Step1: Order the data set

The data set is already ordered: \(3, 3, 3, 5, 6, 9, 9\)

Step2: Find the median

The number of data points \(n = 7\) (odd). The median is the middle value, which is the \(\frac{n + 1}{2}=\frac{7+ 1}{2}=4\)-th value. So the median is \(5\).

Step3: Find the lower quartile (Q1)

The lower half of the data is \(3, 3, 3\) (values below the median). The number of values in the lower half \(n_1=3\) (odd). The lower quartile is the middle value of the lower half, which is the \(\frac{n_1 + 1}{2}=\frac{3+ 1}{2}=2\)-nd value. So Q1 is \(3\).

Step4: Find the upper quartile (Q3)

The upper half of the data is \(6, 9, 9\) (values above the median). The number of values in the upper half \(n_2 = 3\) (odd). The upper quartile is the middle value of the upper half, which is the \(\frac{n_2+ 1}{2}=\frac{3 + 1}{2}=2\)-nd value. So Q3 is \(9\).

Answer:

lower quartile = \(3\)
median = \(5\)
upper quartile = \(9\)