Elena lists the age of all the family members who live in her house below. what is the mean absolute deviation (MAD) of their ages?

9,19,43,55

76, 28, 19, 38

1 answer

To find the Mean Absolute Deviation (MAD) of the ages, we will follow these steps:

  1. Combine the ages into one list. The given ages are: 9, 19, 43, 55, 76, 28, 19, 38.

    Combined list: 9, 19, 43, 55, 76, 28, 19, 38

  2. Calculate the mean (average) of the ages. \[ \text{Mean} = \frac{\text{Sum of all ages}}{\text{Number of ages}} \] Sum of all ages: \[ 9 + 19 + 43 + 55 + 76 + 28 + 19 + 38 = 287 \] Number of ages: \[ 8 \] So the mean is: \[ \text{Mean} = \frac{287}{8} = 35.875 \]

  3. Calculate the absolute deviations from the mean.

    • For each age, subtract the mean and take the absolute value: \[ |9 - 35.875| = 26.875 \] \[ |19 - 35.875| = 16.875 \] \[ |43 - 35.875| = 7.125 \] \[ |55 - 35.875| = 19.125 \] \[ |76 - 35.875| = 40.125 \] \[ |28 - 35.875| = 7.875 \] \[ |19 - 35.875| = 16.875 \] \[ |38 - 35.875| = 2.125 \]
  4. List the absolute deviations: \[ 26.875, 16.875, 7.125, 19.125, 40.125, 7.875, 16.875, 2.125 \]

  5. Calculate the mean of these absolute deviations. \[ \text{Sum of absolute deviations} = 26.875 + 16.875 + 7.125 + 19.125 + 40.125 + 7.875 + 16.875 + 2.125 \] \[ = 137.0 \] Number of absolute deviations: \[ 8 \] Mean Absolute Deviation (MAD): \[ \text{MAD} = \frac{137.0}{8} = 17.125 \]

Thus, the Mean Absolute Deviation (MAD) of their ages is 17.125.