Question

median = 26 minutes
14 16 17 19 22 26 29 37 38 42 47
lower quartile (q1) = 17 minutes
the median separates the data into two halves called the lower half and the upper half.
find the upper quartile, q3, of the data set.
the median of the upper half of the data is the upper quartile (q3).
upper quartile (q3) = minutes

Explanation:

Step1: Identify the upper half of the data

The data set is \(14, 16, 17, 19, 22, 26, 29, 37, 38, 42, 47\). The median is \(26\), so the upper half of the data is \(29, 37, 38, 42, 47\).

Step2: Calculate the median of the upper half

The formula for the median of a set with \(n\) values (where \(n = 5\) for the upper - half) is \(\frac{n + 1}{2}\)th value. Substituting \(n=5\), we get \(\frac{5+1}{2}=3\)rd value.

Answer:

\(38\)