Worksheet: Mean Absolute Deviation

In this worksheet, we will practice finding and interpreting the mean absolute deviation.

Q1:

At an art gallery, Jill hung 14 paintings, Kevin hung 6 paintings, Laurie hung 9 paintings, Meg hung 8 paintings, and Matt hung 9 paintings. Find the mean absolute deviation of the number of paintings hung.

Q2:

The following table shows the number of classes taught by each teacher in the math department at a high school. Find the mean absolute deviation (MAD) of the data set rounded to the nearest hundredth if necessary.

TeacherJamesCharlotteLiamHannah
Number of Classes2425

Q3:

Calculate the mean absolute deviation of 15, 5, 17, 7, 14, 5, 15, and 20. Round your answer to the nearest tenth if necessary.

Q4:

The line plot represents the scores of students in a mathematics test. Which of the following has the greatest mean absolute deviation (MAD)?

  • AB
  • BC
  • CD
  • DA

Q5:

Which pair of data sets is most likely to have the greatest number of values in common?

  • AData set 𝐴 has a mean of =12, data set 𝐵 has a mean of =16, and both sets have a MAD of 8.
  • BData set 𝐴 has a mean of =17, data set 𝐵 has a mean of =14, and both sets have a MAD of 9.
  • CData set 𝐴 has a mean of =12, data set 𝐵 has a mean of =16, and both sets have a MAD of 9.
  • DData set 𝐴 has a mean of =12, data set 𝐵 has a mean of =9, and both sets have a MAD of 2.
  • EData set 𝐴 has a mean of =10, data set 𝐵 has a mean of =16, and both sets have a MAD of 6.

Q6:

The following line plots show the heights, in inches, of different students. Which of them has the smallest mean absolute deviation (MAD)?

  • Aplot A
  • Bplot D
  • Cplot B
  • Dplot C

Q7:

Find the mean absolute deviation of the data in the pictograph shown.

Q8:

Liam and Amelia are comparing their test scores over the last few units. They are trying to decide who is more consistent with respect to grades - meaning who scores pretty close to the same grade on each test. Which of these statistical measures would you recommend they use to decide who is more consistent?

  • Amean
  • Bmode
  • Cmedian
  • Dmean absolute deviation

Q9:

A farmer is testing two different types of plant food in his garden. He used Ultra Feed on five of his plants and Mega Feed on another five. He measured the growth increase of each of the plants and recorded the results, rounded to one decimal place, in the table.

Increase in Growth (cm)
Ultra Feed1.21.40.91.81.7
Mega Feed1.50.61.11.31.0

Find the mean absolute deviation of the growth of the plants fed Ultra Feed.

Find the mean absolute deviation of the growth of the plants fed Mega Feed.

Which feed produces less variability in the growth?

  • AUltra Feed
  • BMega Feed

Q10:

Scarlett and Noah have recorded the number of home runs per game for each of their baseball teams. Compare the mean and the mean absolute deviation (MAD) of the number of home runs of Scarlett’s team to Noah’s team.

  • AScarlett’s team has a smaller mean but a larger MAD.
  • BScarlett’s team has a larger mean and a larger MAD.
  • CScarlett’s team has a larger mean but a smaller MAD.
  • DScarlett’s team has a smaller mean and a smaller MAD.

Q11:

At an art gallery, Jill hung 13 paintings, Kevin hung 8 paintings, Laurie hung 7 paintings, Meg hung 11 paintings, and Matt hung 8 paintings. Find the mean absolute deviation of the number of paintings hung.

Q12:

At an art gallery, Jill hung 4 paintings, Kevin hung 10 paintings, Laurie hung 9 paintings, Meg hung 8 paintings, and Matt hung 9 paintings. Find the mean absolute deviation of the number of paintings hung.

Q13:

At an art gallery, Jill hung 12 paintings, Kevin hung 9 paintings, Laurie hung 9 paintings, Meg hung 12 paintings, and Matt hung 6 paintings. Find the mean absolute deviation of the number of paintings hung.

Q14:

The following table shows the number of classes taught by each teacher in the math department at a high school. Find the mean absolute deviation (MAD) of the data set rounded to the nearest hundredth if necessary.

TeacherEthanHannahDavidNatalie
Number of Classes7948

Q15:

The following table shows the number of classes taught by each teacher in the math department at a high school. Find the mean absolute deviation (MAD) of the data set rounded to the nearest hundredth if necessary.

TeacherAnthonyElizabethLiamJennifer
Number of Classes3948

Q16:

The following table shows the number of classes taught by each teacher in the math department at a high school. Find the mean absolute deviation (MAD) of the data set rounded to the nearest hundredth if necessary.

TeacherDavidMadisonDanielVictoria
Number of Classes3835

Q17:

The following line plots show the heights, in inches, of different students. Which of them has the smallest mean absolute deviation (MAD)?

  • Aplot A
  • Bplot D
  • Cplot B
  • Dplot C

Q18:

The following line plots show the heights, in inches, of different students. Which of them has the smallest mean absolute deviation (MAD)?

  • Aplot C
  • Bplot B
  • Cplot D
  • Dplot A

Q19:

The following line plots show the heights, in inches, of different students. Which of them has the smallest mean absolute deviation (MAD)?

  • Aplot A
  • Bplot D
  • Cplot B
  • Dplot C

Q20:

The following line plots show the heights, in inches, of different students. Which of them has the smallest mean absolute deviation (MAD)?

  • Aplot C
  • Bplot A
  • Cplot D
  • Dplot B

Q21:

The heights of the female volleyball players of the top four teams in the London 2,012 Olympics are given in the table.

Players’ Heights (cm)TeamMeanMean Absolute Deviation (MAD)
BRAUSAJAPKOR
FunctionLiberos169167159168165.83.4
Setters181173159175172.95.0
172170180
Receiver-Attackers186186173192183.15.6
179188175186
Opposites185193185185187.03.0
Middle Blockers196188184190188.93.6
193191186183

Based on these data, is it possible to conclude that the middle blockers are generally taller than the opposites? Why?

  • Ano, because the difference in the mean heights between both functions is significant (greater than the MAD)
  • Bno, because the difference in the mean heights between both functions is not significant (smaller than the MAD)
  • Cyes, because the difference in the mean heights between both functions is not significant (smaller than the MAD)
  • Dyes, because the difference in the mean heights between both functions is significant (greater than the MAD)

Q22:

A study has been conducted to investigate changes in the use of cell phones by seventh-grade students. This year, data on the average number of texts sent every day by about 200 seventh-grade students were gathered and compared to similar data collected two years ago. The table shows a summary of the data in terms of mean and mean absolute deviation.

Average Number of Texts Sent Every DayMeanMean Absolute Deviation (MAD)
Two years ago3916
This year4819

Can the study conclude that the use of texts on cell phones by seventh-grade students has increased in the last two years? Why?

  • Ano, because the difference in the average number of texts is smaller than the variability of the data (about half the MAD)
  • Byes, because the difference in the average number of texts is greater than the variability of the data (more than twice the MAD)
  • Cyes, because the difference in the average number of texts is smaller than the variability of the data (about half the MAD)
  • Dno, because the difference in the average number of texts is greater than the variability of the data (more than twice the MAD)

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