Question

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

Answer 1

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**.