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the number of points that Charleen scored in five basketball games was 8, 14, 10, 7, and 13. Find the mean absolute value deviation of the set of the data. Describe what the mean absolute deviation represents.​

Sagot :

Sethartiolamarceloidn

Answer:

To find the mean absolute deviation (MAD) of Charleen's basketball scores, follow these steps:

1. **Calculate the mean (average) of the scores:**

The scores are: 8, 14, 10, 7, 13

\[

\text{Mean} = \frac{8 + 14 + 10 + 7 + 13}{5} = \frac{52}{5} = 10.4

\]

2. **Find the absolute deviations from the mean for each score:**

- \( |8 - 10.4| = 2.4 \)

- \( |14 - 10.4| = 3.6 \)

- \( |10 - 10.4| = 0.4 \)

- \( |7 - 10.4| = 3.4 \)

- \( |13 - 10.4| = 2.6 \)

3. **Calculate the mean of these absolute deviations:**

\[

\text{MAD} = \frac{2.4 + 3.6 + 0.4 + 3.4 + 2.6}{5} = \frac{12.4}{5} = 2.48

\]

Therefore, the mean absolute deviation of the scores is 2.48.

### What the Mean Absolute Deviation Represents

The mean absolute deviation represents the average distance of each data point from the mean of the data set. In this context, it tells us how much Charleen's basketball scores vary from her average score of 10.4 points per game. A lower MAD would indicate that her scores are closely clustered around the mean, while a higher MAD would suggest more variability in her scoring.

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