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).

Answer 1

To find the Mean Absolute Deviation (MAD) of the test scores, follow these steps:

1. **Calculate the Mean of the Scores**:

First, sum all the scores and then divide by the number of scores.

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

Sum of scores = \( 55 + 60 + 70 + 70 + 75 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 95 + 100 = 1285 \)

Number of scores = 17

Mean = \( \frac{1285}{17} \approx 75.59 \)

2. **Calculate the Absolute Deviations**:

Next, subtract the mean from each score and take the absolute value.

\[
|55 - 75.59| \approx 20.59
\]
\[
|60 - 75.59| \approx 15.59
\]
\[
|70 - 75.59| \approx 5.59
\]
\[
|70 - 75.59| \approx 5.59
\]
\[
|75 - 75.59| \approx 0.59
\]
\[
|75 - 75.59| \approx 0.59
\]
\[
|75 - 75.59| \approx 0.59
\]
\[
|80 - 75.59| \approx 4.41
\]
\[
|80 - 75.59| \approx 4.41
\]
\[
|85 - 75.59| \approx 9.41
\]
\[
|85 - 75.59| \approx 9.41
\]
\[
|85 - 75.59| \approx 9.41
\]
\[
|85 - 75.59| \approx 9.41
\]
\[
|90 - 75.59| \approx 14.41
\]
\[
|90 - 75.59| \approx 14.41
\]
\[
|95 - 75.59| \approx 19.41
\]
\[
|100 - 75.59| \approx 24.41
\]

3. **Sum of Absolute Deviations**:

Sum all the absolute deviations.

Total absolute deviations =
\[
20.59 + 15.59 + 5.59 + 5.59 + 0.59 + 0.59 + 0.59 + 4.41 + 4.41 + 9.41 + 9.41 + 9.41 + 9.41 + 14.41 + 14.41 + 19.41 + 24.41 \approx 267.41
\]

4. **Calculate the Mean Absolute Deviation (MAD)**:

Divide the total of the absolute deviations by the number of scores.

MAD =
\[
\frac{267.41}{17} \approx 15.71
\]

Therefore, the Mean Absolute Deviation (MAD) for Ms. O’Donnell’s class is approximately **15.71**.