Question

here are the ages of 13 people in a coffee shop on a given day:
26, 44, 22, 28, 55, 32, 15, 39, 54, 69, 21, 18, 48
identify the first quartile by finding the middle number on the left side of the median.
if there is no middle number, average the two middle numbers.
15, 18, 21, 22, 26, 28, 32, 39, 44, 48, 54, 55, 69
first quartile (q₁) median (q₂) third quartile (q₃)
?

Explanation:

Step1: Sort the data

First, we sort the data set: \(15, 18, 21, 22, 26, 28, 32, 39, 44, 48, 54, 55, 69\)

Step2: Find the median

Since \(n = 13\) (odd), the median \(Q_2\) is the \(\frac{n + 1}{2}=\frac{13+ 1}{2}=7^{th}\) value. So \(Q_2 = 32\)

Step3: Find the first - quartile

The lower half of the data (values less than \(32\)) is \(15, 18, 21, 22, 26, 28\). Since \(n = 6\) (even) for the lower half, the first quartile \(Q_1=\frac{3^{rd}+4^{th}}{2}\)
\(Q_1=\frac{21 + 22}{2}=\frac{43}{2}=21.5\)

Answer:

\(21.5\)