Question

Here are the science test scores from Ms. O’Donnell’s class:

55, 60, 70, 70, 75, 75, 75, 80, 80, 85, 85, 85, 85, 90, 90, 95, 100

Find the mean absolute deviation (MAD).

(1 point)
The MAD is
.

Answer 1

To calculate the mean absolute deviation (MAD), follow these steps:

1. Find the mean (average) of the scores.
2. Calculate the absolute deviations from the mean for each score.
3. Find the average of those absolute deviations.

### Step 1: Calculate the Mean

The scores are:

55, 60, 70, 70, 75, 75, 75, 80, 80, 85, 85, 85, 85, 90, 90, 95, 100

To find the mean:

\[
\text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}}
\]

Sum of all scores:

\[
55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1305
\]

Number of scores: 17

\[
\text{Mean} = \frac{1305}{17} \approx 76.76
\]

### Step 2: Calculate Absolute Deviations

Now, we find the absolute deviation for each score from the mean:

- |55 - 76.76| = 21.76
- |60 - 76.76| = 16.76
- |70 - 76.76| = 6.76
- |70 - 76.76| = 6.76
- |75 - 76.76| = 1.76
- |75 - 76.76| = 1.76
- |75 - 76.76| = 1.76
- |80 - 76.76| = 3.24
- |80 - 76.76| = 3.24
- |85 - 76.76| = 8.24
- |85 - 76.76| = 8.24
- |85 - 76.76| = 8.24
- |85 - 76.76| = 8.24
- |90 - 76.76| = 13.24
- |90 - 76.76| = 13.24
- |95 - 76.76| = 18.24
- |100 - 76.76| = 23.24

### Step 3: Calculate the Mean of Absolute Deviations

Sum of absolute deviations:

\[
21.76 + 16.76 + 6.76 + 6.76 + 1.76 + 1.76 + 1.76 + 3.24 + 3.24 + 8.24 + 8.24 + 8.24 + 8.24 + 13.24 + 13.24 + 18.24 + 23.24 = 172.00
\]

Now, divide by the number of scores (17):

\[
\text{MAD} = \frac{172.00}{17} \approx 10.12
\]

So, the mean absolute deviation (MAD) is approximately **10.12**.