Question

Jill bought supplies for a class project and brought the receipt to school. The 7 items cost:
$3.20$3.00$7.40$1.70$9.20$5.30$5.90
What was the mean absolute deviation of the prices of the items?

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 prices of the items, we will follow these steps:

1. **List the prices**:
- $3.20, $3.00, $7.40, $1.70, $9.20, $5.30, $5.90$

2. **Calculate the mean (average)**:
\[
\text{Mean} = \frac{\text{Sum of prices}}{\text{Number of items}}
\]
- First, find the sum of the prices:
\[
3.20 + 3.00 + 7.40 + 1.70 + 9.20 + 5.30 + 5.90 = 35.70
\]
- There are 7 items, so:
\[
\text{Mean} = \frac{35.70}{7} = 5.10
\]

3. **Calculate the absolute deviations from the mean**:
- For each price, subtract the mean and take the absolute value:
\[
|3.20 - 5.10| = | -1.90| = 1.90
\]
\[
|3.00 - 5.10| = | -2.10| = 2.10
\]
\[
|7.40 - 5.10| = | 2.30| = 2.30
\]
\[
|1.70 - 5.10| = | -3.40| = 3.40
\]
\[
|9.20 - 5.10| = | 4.10| = 4.10
\]
\[
|5.30 - 5.10| = | 0.20| = 0.20
\]
\[
|5.90 - 5.10| = | 0.80| = 0.80
\]

4. **Sum of absolute deviations**:
\[
1.90 + 2.10 + 2.30 + 3.40 + 4.10 + 0.20 + 0.80 = 14.80
\]

5. **Calculate the mean absolute deviation**:
\[
\text{MAD} = \frac{\text{Sum of absolute deviations}}{\text{Number of items}} = \frac{14.80}{7} = 2.11
\]

6. **Round the MAD to the nearest ten cents**:
- The value \(2.11\) is already at two decimal places, therefore it remains as \(2.11\).

Thus, the mean absolute deviation (MAD) is:

\[
\boxed{2.11}
\]