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Elena lists the ages of all the family members who live in her house. What is the mean absolute deviation of their ages.

Ages 9, 13, 43, 55.
A. 28
B. 38
C. 76
D. 19

1 answer

To find the mean absolute deviation (MAD) of the ages 9, 13, 43, and 55, we can follow these steps:

  1. Calculate the mean (average) of the ages: \[ \text{Mean} = \frac{\text{Sum of ages}}{\text{Number of ages}} = \frac{9 + 13 + 43 + 55}{4} = \frac{120}{4} = 30 \]

  2. Calculate the absolute deviations from the mean: \[ |9 - 30| = 21 \] \[ |13 - 30| = 17 \] \[ |43 - 30| = 13 \] \[ |55 - 30| = 25 \]

  3. Calculate the mean of these absolute deviations: \[ \text{Mean Absolute Deviation (MAD)} = \frac{|9 - 30| + |13 - 30| + |43 - 30| + |55 - 30|}{4} = \frac{21 + 17 + 13 + 25}{4} = \frac{76}{4} = 19 \]

Thus, the mean absolute deviation of their ages is \( 19 \).

The answer is D. 19.