MSTAR Practice Worksheet

Lesson 2-9: Describe Data by Mean Absolute Deviation

Grade 6 Mathematics · Standard 6.DS.6c

Name: Date:

These are MSTAR-style questions written for this curriculum to rehearse the format. They are not official Maryland assessment items. MSTAR — Maryland's new state test, first given in spring 2027 — uses the same kinds of questions you see here: selected response, select-all, two-part evidence questions, and written responses.

Part A — Skills Check

Warm up with the lesson's core skills — one best answer each.

Question 1Selected response · 1 point

The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?

A4
B−4
C11
D26

Question 2Selected response · 1 point

A data set has absolute deviations of 3, 1, 5, 2, 4. What is the MAD?

Question 3Selected response · 1 point

The mean of a data set is 20. A value is 26. What is the absolute deviation?

A6
B−6
C26
D46

Question 4Selected response · 1 point

Team A has MAD = 2.1 points. Team B has MAD = 6.8 points. Which team is more consistent?

ATeam B — higher MAD means better performance
BBoth are equally consistent
CCannot tell from MAD alone
DTeam A — lower MAD means scores are closer to the mean

Question 5Selected response · 1 point

Two runners have the same average time of 60 seconds. Runner A's MAD is 1.2 seconds. Runner B's MAD is 5.8 seconds. Which runner is the coach more likely to pick for a relay race that needs a reliable time?

ARunner B — higher MAD means faster potential
BEither — they have the same average
CRunner A — lower MAD means more consistent times
DNeither — MAD doesn't matter for relay races

Question 6Selected response · 1 point

A guard scored 2, 4, 6, 8 points in four scrimmages, so the mean is 5 points. The distances from the mean are 3, 1, 1, 3. What is the mean absolute deviation (MAD)?

Part B — Test-Format Questions

These match the state test's formats: two-part questions, select-all, and written responses.

Question 7Two-part question

Part A

A data set is 3, 5, 9, 11 with a mean of 7. What is the mean absolute deviation?

Fill in the bubble next to the one best answer.

Part B

Answer Part A before Part B — Part B asks about your reasoning.

Why are the DISTANCES from the mean used rather than the signed differences?

ADistances are easier to add.
BNegative numbers cannot be divided.
CThe signed differences always add to zero, so they would give a MAD of 0 for every data set.
DThe mean is always larger than every value.

Question 8Written response · 2 points

Type II Reasoning: The Deviations That Cancel

Sofia found the MAD of 3, 5, 9, 11 (mean 7). She used the signed differences −4, −2, 2, 4, added them to get 0, and concluded 'the MAD is 0, so there is no variability.'

Explain Sofia's misconception and give the correct MAD.

Write your answer in complete sentences. Show or explain your mathematical thinking.

Part C — Show Your Thinking

Answer in writing, the way the state test's constructed responses work.

Question 9Written response · 2 points

Two basketball teams both average 75 points per game. Team A's last 5 scores: 73, 76, 74, 77, 75. Team B's last 5 scores: 60, 90, 65, 85, 75. Calculate the MAD for each team and explain which team a coach would prefer if they need predictable scoring.

Write your answer in complete sentences. Show or explain your mathematical thinking.