Question

A data set has 10 values. • The mean of the data in the set is 12. • The mean absolute deviation of the data in the set is 4. Which statement about the values in the data set must be true? Each value in the data set varies from 12 by exactly 4. Each value in the data set varies from 12 by an average of 4. No values in the data set are less than 8 or greater than 16. Half of the values in the data set are 8 and half of the values in the data set are 16.

Answer 1

The statement that must be true about the values in the data set is: "No values in the data set are less than 8 or greater than 16."

Explanation:

Mean is the average value of a dataset. In this case, the mean of the data set is given as 12.

Mean absolute deviation (MAD) measures the average distance between each data point and the mean of the dataset. In this case, the MAD is given as 4.

If each value in the data set varied from 12 by exactly 4, then the mean absolute deviation would be 4. However, in this case, the given mean absolute deviation is 4, which means the average deviation is 4, but individual values can deviate in both positive and negative directions.

The statement that half of the values in the data set are 8 and half of the values are 16 cannot be concluded based on the given information. The mean of 12 does not imply that half the values are 8 and the other half are 16.

Therefore, the only statement that can be confirmed as true based on the given information is: "No values in the data set are less than 8 or greater than 16."