Question

which statements about the data sets are true? check all that apply.
□ the data for the group that plays an instrument are more spread out than the data for the group that did not play an instrument.
□ the data for the group that plays an instrument are more clustered around the mean than the data for the group that did not play an instrument.
□ the mean absolute deviation for students who play an instrument is 1.
□ the data for the group that does not play an instrument are more spread out than the data for the group that does play an instrument
□ the mean absolute deviation for the group of students who do not play an instrument is 2.
□ the data for the group that does not play an instrument are more clustered around the mean than the data for the group that does play an instrument.

Explanation:

To solve this, we analyze each statement based on the concept of mean absolute deviation (MAD), which measures data spread (higher MAD means more spread out, lower MAD means more clustered around the mean).

Analyzing Each Statement:

1. "The data for the group that plays an instrument are more spread out than the data for the group that did not play an instrument."

If the group playing an instrument has a larger MAD, this is true. But typically, non - instrument groups might have more spread (or vice - versa, but we assume the context here). However, let's check others.

1. "The data for the group that plays an instrument are more clustered around the mean than the data for the group that did not play an instrument."

Clustered data has a smaller MAD. If instrument - playing group has smaller MAD, this is true (opposite of the first statement, so only one of 1 or 2 can be true).

1. "The mean absolute deviation for students who play an instrument is 1."

We don't have data to confirm this, so we can't assume.

1. "The data for the group that does not play an instrument are more spread out than the data for the group that does play an instrument."

This is the opposite of statement 1. If non - instrument group has larger MAD, this is true.

1. "The mean absolute deviation for the group of students who do not play an instrument is 2."

We don't have data to confirm this, so we can't assume.

1. "The data for the group that does not play an instrument are more clustered around the mean than the data for the group that does play an instrument."

This is the opposite of statement 2. If non - instrument group is more clustered, instrument group is more spread (and vice - versa).

From typical scenarios (e.g., instrument - playing students might have more consistent data, so non - instrument data is more spread, and instrument data is more clustered), the true statements are:

• The data for the group that plays an instrument are more clustered around the mean than the data for the group that did not play an instrument.
• The data for the group that does not play an instrument are more spread out than the data for the group that does play an instrument.

Answer:

• The data for the group that plays an instrument are more clustered around the mean than the data for the group that did not play an instrument.
• The data for the group that does not play an instrument are more spread out than the data for the group that does play an instrument.

(Note: If we assume the MAD values given (1 for instrument, 2 for non - instrument), then statements "The mean absolute deviation for students who play an instrument is 1", "The mean absolute deviation for the group of students who do not play an instrument is 2", "The data for the group that plays an instrument are more clustered around the mean than the data for the group that did not play an instrument", and "The data for the group that does not play an instrument are more spread out than the data for the group that does play an instrument" are true.)