Question

Judith went around the neighborhood collecting spare change for charity. The 7 families gave:
$3.50$9.80$3.50$9.30$8.60$9.40$2.80
What was the mean absolute deviation of the amounts of change given?

If the answer is a decimal, round it to the nearest ten cents.

mean absolute deviation (MAD): $

Answer 1

To calculate the mean absolute deviation (MAD) of the amounts collected, we'll follow these steps:

1. **List the amounts given**:
- $3.50
- $9.80
- $3.50
- $9.30
- $8.60
- $9.40
- $2.80

2. **Calculate the mean of the amounts**:
\[
\text{Mean} = \frac{\text{Sum of amounts}}{\text{Number of families}}
\]

First, sum the amounts:
\[
3.50 + 9.80 + 3.50 + 9.30 + 8.60 + 9.40 + 2.80 = 56.90
\]

Now, divide by the number of families (7):
\[
\text{Mean} = \frac{56.90}{7} \approx 8.13
\]

3. **Calculate the absolute deviations from the mean**:
\[
|3.50 - 8.13| \approx 4.63
\]
\[
|9.80 - 8.13| \approx 1.67
\]
\[
|3.50 - 8.13| \approx 4.63
\]
\[
|9.30 - 8.13| \approx 1.17
\]
\[
|8.60 - 8.13| \approx 0.47
\]
\[
|9.40 - 8.13| \approx 1.27
\]
\[
|2.80 - 8.13| \approx 5.33
\]

4. **Sum the absolute deviations**:
\[
4.63 + 1.67 + 4.63 + 1.17 + 0.47 + 1.27 + 5.33 = 19.17
\]

5. **Calculate the mean absolute deviation**:
\[
\text{MAD} = \frac{\text{Sum of absolute deviations}}{\text{Number of families}}
\]
\[
\text{MAD} = \frac{19.17}{7} \approx 2.74
\]

6. **Round to the nearest ten cents**:
\[
\text{Rounded MAD} \approx 2.74
\]

Thus, the mean absolute deviation (MAD) of the amounts of change given is **$2.74**.