Task Sets: Informally assess the degree of visual overlap of two numerical data distributions - Common Core Math - Grade 7

Recall / Warm-Up

The data set is 4, 6, 7, 9, 14. What is the mean?

$7$

$8$

$9$

$10$

Evaluate $|8.5 - 12|$ .

$-3.5$

$3.5$

$20.5$

$4.0$

Compute the mean of the data set: 5, 7, 7, 9, 10, 10.

Fluency Practice

The data set is 3, 5, 6, 7, 9, and the mean is 6. Compute the Mean Absolute Deviation (MAD).

Group A has a mean of 24. Group B has a mean of 18. The average MAD for both groups is 3. Compute the MAD-multiple (difference in means divided by average MAD).

Two data distributions have a MAD-multiple of 2.1. Which statement is most accurate?

The distributions completely separate — there is no overlap between them.

The distributions are noticeably separated — most values in one group exceed most values in the other, though some overlap may still exist near the boundary.

The distributions have about the same center — the difference is not meaningful.

The distributions substantially overlap — most values fall in the same region.

The data set is 8, 10, 12, 14, 16, 18, 20, 22. Compute the MAD.

A MAD-multiple of 0.5 most likely indicates which of these?

Noticeable separation — most values in the two groups are distinctly different.

Substantial overlap — the two distributions mostly occupy the same region of the number line.

No variability within either group.

The two groups have identical means.

Comparing Two Data Distributions: MAD and Overlap

Recall / Warm-Up

Fluency Practice