Digits, Grade 8, Volume 2, Homework Helper

#### Part 1

Example Analyzing Deviations of Data Sets

The table shows the maximum lifespan of various animals. The mean absolute deviation is 48. Determine whether each statement is true or false.

• a. The mean lifespan is 58 years.

• b. The deviation of a dolphin's lifespan from the mean is +6.

• c. The absolute deviation of a whale's lifespan from the mean is greater than the absolute deviation of a mouse's lifespan from the mean.

• d. A cat's lifespan deviates from the mean more than average. Solution

• a. True.

table with 3 rows and 2 columns , row1 column 1 , meanlifespan , column 2 equals . fraction 30 plus 24 plus 52 plus 65 plus 21 plus 4 plus 9 plus 26 plus 138 plus 211 , over 10 end fraction , row2 column 1 , , column 2 equals , 580 over 10 , row3 column 1 , , column 2 equals 58 , end table

• b. False. The lifespan of a dolphin, 52 years, is less than the mean lifespan, 58 years, so the deviation is negative.

52−58=−6

The deviation of a dolphin's lifespan from the mean is −6.

• c. True. The lifespan of a whale is 211 years.

211−58 = 153

So the absolute deviation of a whale's lifespan from the mean is 153.

The lifespan of a mouse is 4 years. So the absolute deviation of a mouse's lifespan from the mean is 54.

The absolute deviation of a whale's lifespan from the mean is greater than the absolute deviation of a mouse's lifespan from the mean.

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