We are given a data set of the number of sandwiches sold each day: $50, 109, 127, 100, 74, 66, 150, 113, 88$. We need to identify which of the two provided box plots represents this data.

1. Problem Description

We are given a data set of the number of sandwiches sold each day: $50, 109, 127, 100, 74, 66, 150, 113, 88$. We need to identify which of the two provided box plots represents this data.

2. Solution Steps

To determine the correct box plot, we need to calculate the following statistics for the given data:

- Minimum value

- First quartile (Q1)

- Median (Q2)

- Third quartile (Q3)

- Maximum value

First, let's sort the data in ascending order: $50, 66, 74, 88, 100, 109, 113, 127, 150$.

- Minimum value: $50$

- Maximum value: $150$

- Median (Q2): The median is the middle value. Since there are 9 data points, the middle value is the 5th value, which is $100$.

- First quartile (Q1): The first quartile is the median of the lower half of the data. The lower half is $50, 66, 74, 88$. The median of this is $\frac{66+74}{2} = \frac{140}{2} = 70$.

- Third quartile (Q3): The third quartile is the median of the upper half of the data. The upper half is $109, 113, 127, 150$. The median of this is $\frac{113+127}{2} = \frac{240}{2} = 120$.

So, the five-number summary is:

- Minimum: $50$

- Q1: $70$

- Median: $100$

- Q3: $120$

- Maximum: $150$

Now, let's examine the two box plots:

- The first box plot appears to have the following values approximately:

Minimum: $50$

Q1: $70$

Median: $100$

Q3: $120$

Maximum: $150$

This matches our calculated values.

- The second box plot appears to have the following values approximately:

Minimum: $50$

Q1: $80$

Median: $95$

Q3: $110$

Maximum: $150$

This does not match our calculated values.

Therefore, the first box plot correctly represents the data.

3. Final Answer

The first box plot represents the data.