Question

shanice collects data on the number of minutes a scooter is rented by different riders. median = 26 minutes 14 16 17 19 22 26 29 37 38 42 47 find the lower quartile, q1, of the data set. lower quartile (q1) = minutes the median separates the data into two halves called the lower half and the upper half. the median of the lower half of the data is the lower quartile (q1).

Explanation:

Step1: Determine the lower half of the data

The data set is \(14, 16, 17, 19, 22, 26, 29, 37, 38, 42, 47\). The median is the \(6^{th}\) value (\(n = 11\), median position \(=\frac{n + 1}{2}=\frac{11+ 1}{2}=6\)). The lower half of the data is \(14, 16, 17, 19, 22\).

Step2: Calculate the median of the lower half

For the data set \(14, 16, 17, 19, 22\) (\(n = 5\)), the median position \(=\frac{n + 1}{2}=\frac{5+1}{2}=3\). The \(3^{rd}\) value in the ordered set \(14, 16, 17, 19, 22\) is \(17\).

Answer:

\(17\)