The stem-and-leaf diagram shows the daily number of customers over a period of one month at Branch A of a Food Outlet.

1. Identify the middle positions and read the corresponding values from the ordered stem-and-leaf diagram.

There are $30$ values in the stem-and-leaf diagram.

For an even number of values, the median is the average of the $15$th and $16$th values.

From the ordered diagram, the $15$th value is $33$ and the $16$th value is $34$.

$\text{Median}=\frac{33+34}{2}=33.5$

1. Identify the positions of the lower and upper quartiles in the ordered data.

There are $30$ values in the stem-and-leaf diagram.

Since $30$ is even, split the ordered data into two halves of $15$ values each.

$Q_1$ is the median of the lower $15$ values, so it is the $8$th value.

$Q_3$ is the median of the upper $15$ values, so it is the $23$rd value overall.

2. Read the quartiles and calculate the interquartile range.

From the stem-and-leaf diagram,

$Q_1 = 22$ and $Q_3 = 47$.

$\text{Interquartile range} = Q_3 - Q_1 = 47 - 22 = 25$

1. Compare the medians and justify the choice of branch.

Branch A: median $=33.5$, interquartile range $=25$.

Branch B: median $=27$, interquartile range $=23$.

Since Branch A has a higher median number of customers, it has a higher typical daily number of customers. Hence Branch A should be expanded.