Let's go through each of the parts based on the image you uploaded.

Part (a)

This is about the spread of the data set. The relevant information here is the IQR (Interquartile Range), which is 3 (given in the summary values table). The spread of the middle 50% of the data is represented by the IQR. Therefore, the correct option is:

• The middle half of the data set is 3 units wide. (This is the IQR.)

Part (b)

This is asking about the center of the data set. The relevant values here are the mean (52) and median (53). Since both the mean and the median are close to each other, the best description of the center of the data is based on these values. The correct option is:

• Based on the mean and median, we see that the "average" number of people served was about 52 or 53.

Part (c)

This asks you to choose the graph that best fits the shape of the summary values. The data does not appear to be symmetric (the mean and median are close, but the IQR and range suggest some skewness). Graph 2 shows a skewed distribution, which fits this dataset better than the symmetric Graph 1. Thus, the correct option is:

• Graph 2 (The data set is not symmetric.)

Would you like further explanation on any of these parts?

Additional Questions:

1. What is the difference between IQR and range in data sets?
2. How does the mean and median indicate whether data is skewed or symmetric?
3. Why does a small IQR suggest that the middle values of the data are clustered closely?
4. What other summary statistics can help describe the spread of data?
5. How does understanding the shape of the data help in interpreting it?

Tip: The IQR is more resistant to outliers than the range, making it a better measure for understanding the "typical" spread of data.