Question

what is the upper and lower quartile of this set of data?
15, 19, 20, 25, 31, 38, 41
○ lower quartile: 19
upper quartile: 25
○ lower quartile: 25
upper quartile: 38
○ lower quartile: 19
upper quartile: 38
○ lower quartile: 15
upper quartile: 41

Explanation:

Step1: Find the median

The data set is \(15, 19, 20, 25, 31, 38, 41\). The median (middle value) is the \(4^{th}\) value. So, the median \(Q_2 = 25\).

Step2: Find the lower half

The lower half of the data is \(15, 19, 20\). The median of the lower half (lower quartile \(Q_1\)) is the \(2^{nd}\) value. So, \(Q_1=19\).

Step3: Find the upper half

The upper half of the data is \(31, 38, 41\). The median of the upper half (upper quartile \(Q_3\)) is the \(2^{nd}\) value of the upper - half. So, \(Q_3 = 38\).

Answer:

lower quartile: 19, upper quartile: 38 (the third option)