Question

in the data set below, what are the lower quartile, the median, and the upper quartile? 36 36 53 59 93 lower quartile = median = upper quartile =

Explanation:

Step1: Find the median

The data set is \(36,36,53,59,93\). The median is the middle value. Since there are \(n = 5\) values, the median is the \(\frac{n + 1}{2}=\frac{5+1}{2}=3\)rd value.
So, the median is \(53\).

Step2: Find the lower quartile

The lower half of the data set (excluding the median) is \(36,36\). The lower quartile is the median of the lower - half. For \(n = 2\) values, the median is \(\frac{36 + 36}{2}=36\).

Step3: Find the upper quartile

The upper half of the data set (excluding the median) is \(59,93\). The upper quartile is the median of the upper - half. For \(n=2\) values, the median is \(\frac{59 + 93}{2}=76\).

Answer:

lower quartile \(=36\)
median \(=53\)
upper quartile \(=76\)