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…

Answer:

$21$

Explanation:

Step1: Arrange data in order

$15, 18, 21, 22, 26, 28, 32, 39, 44, 48, 54, 55, 69$

Step2: Find the median position

There are $n = 13$ data - points. The median position is $\frac{n + 1}{2}=\frac{13+1}{2}=7$th value, which is $32$.

Step3: Consider the left - hand side of the median

The left - hand side of the median consists of the values $15, 18, 21, 22, 26, 28$. There are $n_1=6$ values.

Step4: Find the first - quartile position

The position of the first quartile for an even - numbered set of data on the left - hand side of the median is $\frac{n_1 + 1}{2}=\frac{6 + 1}{2}=3.5$. So, we take the average of the 3rd and 4th values.

Step5: Calculate the first quartile

The 3rd value is $21$ and the 4th value is $22$. The first quartile $Q_1=\frac{21 + 22}{2}=21.5$. But if we follow the method of just taking the middle number of the left - hand side (when we consider the non - average method as per the problem's instruction), for the set $15, 18, 21, 22, 26, 28$, the middle number of the left - hand side of the median is the 3rd number, which is $21$.