Use the table to answer the question.

2 (median)

To determine whether the mean or median best describes the shape of the data set of the number of free throws made by the basketball team, we need to first understand what each represents.

1. Mean: The mean is calculated by summing up all the data points and dividing it by the total number of data points. It is the average of the data set.

2. Median: The median is the middle value of the data set when it is arranged in ascending or descending order. If there is an even number of data points, the median is the average of the two middle values.

In this case, the data set is as follows:

Game: 1 2 3 4 5 6 7
FTs: 4 14 5 7 19 15 6

To find the mean, we sum up all the values and divide by the total number of values:
(4 + 14 + 5 + 7 + 19 + 15 + 6) / 7 = 70 / 7 = 10

To find the median, we need to arrange the data set in ascending order:
4, 5, 6, 7, 14, 15, 19

Since there are an odd number of data points, the median is the middle value, which is 7.

Comparing the mean and median, we can see that the mean is 10, while the median is 7.

Therefore, to best describe the shape of the data set, we would choose 1 for mean.

To determine whether the mean or median better describes the shape of the data set for the number of free throws made, we need to consider the distribution of the values. If the data is symmetrically distributed, the mean and median will be similar. However, if there are outliers or the data is skewed, the median may be a better measure of central tendency because it is not affected by extreme values.

Let's calculate both:

The **mean** is the average of the numbers:
$$ \text{Mean} = \frac{4 + 14 + 5 + 7 + 19 + 15 + 6}{7} = \frac{70}{7} = 10 $$

The **median** is the middle value when the numbers are listed in order:
The ordered list is 4, 5, 6, 7, 14, 15, 19. The median value, which is the fourth value, is 7.

Given that the data set has a couple of high values (14, 15, and 19), which could skew the mean, the median might be a better representation of the central tendency of this data set.

Therefore, the answer is **2 for median**. It best describes the shape of the data set for the number of free throws made by the basketball team.