Coach Jericho recorded the number of shots made by the starters on the 6th grade and 8th grade boys’ basketball team during the season.

6th Grade
22, 15, 17, 18, 20

8th
58, 58, 52, 55, 53

Which statement is true? Select two answers.

A.
The data spread for the 8th graders is greater than for the 6th graders.*******

B.
Both sets of data have the same mean.

C.
The data set distribution for the 6th grade players is skewed right.

D.
The mean for the 8th grade players is 3 times the mean for the 6th grade players.

E.
The data set distribution for the 8th grade players is symmetric.*******

D,E

Agree with A but not E.

To determine which statements are true, we need to analyze the given data sets for the 6th grade and 8th grade boys' basketball teams.

To find the data spread, we can calculate the range of each data set by subtracting the smallest value from the largest value.

For the 6th-grade team:
The smallest value is 15 and the largest value is 22.
So, the range for the 6th-grade team is 22 - 15 = 7.

For the 8th-grade team:
The smallest value is 52 and the largest value is 58.
So, the range for the 8th-grade team is 58 - 52 = 6.

As the range, or data spread, for the 6th-grade team (7) is greater than that of the 8th-grade team (6), statement A is true.

To determine if the data sets have the same mean, we can calculate the mean (average) of each data set by summing all the values and dividing by the number of observations (in this case, the number of shots made).

For the 6th-grade team:
Sum of all values = 22 + 15 + 17 + 18 + 20 = 92.
Number of observations = 5.
Mean = 92/5 = 18.4.

For the 8th-grade team:
Sum of all values = 58 + 58 + 52 + 55 + 53 = 276.
Number of observations = 5.
Mean = 276/5 = 55.2.

Since the means for the two data sets (18.4 for 6th grade and 55.2 for 8th grade) are different, statement B is false.

To determine the distribution shape, we can plot the data sets on a number line or construct a histogram. However, from the information provided, we cannot definitively conclude the shape of the distribution for either data set. Therefore, statement C cannot be determined from the given information.

To determine if the mean for the 8th grade players is three times the mean for the 6th grade players, we can calculate three times the mean for the 6th grade players and compare it to the mean for the 8th grade players.

Three times the mean for the 6th grade players:
3 * 18.4 = 55.2.

The mean for the 8th grade players is 55.2. Therefore, statement D is true.

Finally, to determine if the data set distribution for the 8th grade players is symmetric, we would need to analyze the data set further, potentially through visualization techniques such as constructing a histogram. The given information is not sufficient to determine the symmetry of the distribution for the 8th grade players. Therefore, statement E cannot be determined from the given information.

In summary, the true statements are:
A. The data spread for the 8th graders is greater than for the 6th graders.
D. The mean for the 8th grade players is three times the mean for the 6th grade players.