Question

in the data set below, what are the lower quartile, the median, and the upper quartile?
23 26 29 65 68 71 74
lower quartile =
median =
upper quartile =

Explanation:

Step1: Order the data set

The data set is already ordered: \(23, 26, 29, 65, 68, 71, 74\)

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 term. So the median is \(65\).

Step3: Find the lower quartile

The lower half of the data set (excluding the median) is \(23, 26, 29\). The lower quartile (Q1) is the median of this lower half. For \(n = 3\) (odd), the median is the \(\frac{3 + 1}{2}=2\)-nd term. So Q1 is \(26\).

Step4: Find the upper quartile

The upper half of the data set (excluding the median) is \(68, 71, 74\). The upper quartile (Q3) is the median of this upper half. For \(n = 3\) (odd), the median is the \(\frac{3+ 1}{2}=2\)-nd term. So Q3 is \(71\).

Answer:

lower quartile = \(26\)
median = \(65\)
upper quartile = \(71\)