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.