Question

Ernest counted the number of fish kept in 7 tanks at the pet store. He counted:
74 fish49 fish47 fish56 fish73 fish41 fish31 fish
What was the mean absolute deviation of the numbers of fish?

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

mean absolute deviation (MAD):
fish

Answer 1

To find the mean absolute deviation (MAD) of the number of fish in the 7 tanks, we follow these steps:

1. **Calculate the Mean:**
First, we need to calculate the mean (average) number of fish.

The numbers of fish in the tanks are:
- 74
- 49
- 47
- 56
- 73
- 41
- 31

Now, we add these numbers together:

\[
74 + 49 + 47 + 56 + 73 + 41 + 31 = 371
\]

Next, we divide by the number of tanks (7):

\[
\text{Mean} = \frac{371}{7} \approx 53
\]

2. **Calculate the Absolute Deviations:**
Now we find the absolute deviations from the mean for each tank:

- \(|74 - 53| = 21\)
- \(|49 - 53| = 4\)
- \(|47 - 53| = 6\)
- \(|56 - 53| = 3\)
- \(|73 - 53| = 20\)
- \(|41 - 53| = 12\)
- \(|31 - 53| = 22\)

This gives us the absolute deviations:
- 21, 4, 6, 3, 20, 12, 22

3. **Calculate the Mean of the Absolute Deviations:**
Now we sum the absolute deviations:

\[
21 + 4 + 6 + 3 + 20 + 12 + 22 = 88
\]

Next, we divide by the number of tanks (7):

\[
\text{MAD} = \frac{88}{7} \approx 12.57142857142857
\]

4. **Round to the Nearest Tenth:**
Finally, we round the result to the nearest tenth:

\[
\text{MAD} \approx 12.6
\]

Therefore, the mean absolute deviation of the numbers of fish is approximately \( \boxed{12.6} \).