# Worksheet: Mean Absolute Deviation

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

**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 has a mean of , data set has a mean of , and both sets have a MAD of 8.
- BData set has a mean of , data set has a mean of , and both sets have a MAD of 9.
- CData set has a mean of , data set has a mean of , and both sets have a MAD of 9.
- DData set has a mean of , data set has a mean of , and both sets have a MAD of 2.
- EData set has a mean of , data set has a mean of , 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 Feed | 1.2 | 1.4 | 0.9 | 1.8 | 1.7 |

Mega Feed | 1.5 | 0.6 | 1.1 | 1.3 | 1.0 |

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.

**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: **

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

**Q20: **

- 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) | Team | Mean | Mean Absolute Deviation (MAD) | ||||
---|---|---|---|---|---|---|---|

BRA | USA | JAP | KOR | ||||

Function | Liberos | 169 | 167 | 159 | 168 | 165.8 | 3.4 |

Setters | 181 | 173 | 159 | 175 | 172.9 | 5.0 | |

172 | 170 | 180 | |||||

Receiver-Attackers | 186 | 186 | 173 | 192 | 183.1 | 5.6 | |

179 | 188 | 175 | 186 | ||||

Opposites | 185 | 193 | 185 | 185 | 187.0 | 3.0 | |

Middle Blockers | 196 | 188 | 184 | 190 | 188.9 | 3.6 | |

193 | 191 | 186 | 183 |

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 Day | Mean | Mean Absolute Deviation (MAD) |
---|---|---|

Two years ago | 39 | 16 |

This year | 48 | 19 |

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)