Question

Dave bought 6 items at a back-to-school sale. The items cost:
$8.40$8.70$4.00$7.70$5.40$6.60
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 find the mean absolute deviation (MAD) of the prices of the items, follow these steps:

1. **Calculate the mean (average) of the prices.**

The prices of the items are:
- $8.40
- $8.70
- $4.00
- $7.70
- $5.40
- $6.60

First, we need to sum these prices:

\[
8.40 + 8.70 + 4.00 + 7.70 + 5.40 + 6.60 = 40.80
\]

Next, we calculate the mean by dividing the total by the number of items:

\[
\text{Mean} = \frac{40.80}{6} = 6.80
\]

2. **Calculate the absolute deviations from the mean.**

Now we calculate the absolute deviation of each price from the mean ($6.80$):

- For $8.40$:
\[
|8.40 - 6.80| = 1.60
\]

- For $8.70$:
\[
|8.70 - 6.80| = 1.90
\]

- For $4.00$:
\[
|4.00 - 6.80| = 2.80
\]

- For $7.70$:
\[
|7.70 - 6.80| = 0.90
\]

- For $5.40$:
\[
|5.40 - 6.80| = 1.40
\]

- For $6.60$:
\[
|6.60 - 6.80| = 0.20
\]

3. **Sum the absolute deviations.**

Now we add all the absolute deviations:

\[
1.60 + 1.90 + 2.80 + 0.90 + 1.40 + 0.20 = 8.80
\]

4. **Calculate the mean absolute deviation.**

Finally, we find the mean absolute deviation by dividing the total absolute deviation by the number of items:

\[
\text{MAD} = \frac{8.80}{6} \approx 1.46667
\]

Now we round it to the nearest ten cents:

\[
\text{MAD} \approx 1.47
\]

Thus, the mean absolute deviation (MAD) of the prices of the items is:

\[
\text{mean absolute deviation (MAD)}: \boxed{1.47}
\]