Question

Determine the mean absolute deviation of the following dataset. Round your answer to the nearest tenth.

{134,138,150,155,158,165}

(1 point)
Responses

9.3
9.3

150
150

11.2
11.2

56
56
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Answer 1

To calculate the mean absolute deviation (MAD) of the dataset {134, 138, 150, 155, 158, 165}, follow these steps:

1. **Calculate the mean of the dataset**:
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{134 + 138 + 150 + 155 + 158 + 165}{6} = \frac{1000}{6} \approx 166.67
\]

2. **Calculate the absolute deviations from the mean**:
\[
|134 - 150| = 16
\]
\[
|138 - 150| = 12
\]
\[
|150 - 150| = 0
\]
\[
|155 - 150| = 5
\]
\[
|158 - 150| = 8
\]
\[
|165 - 150| = 15
\]

3. **Compute the mean absolute deviation**:
\[
\text{MAD} = \frac{\text{Sum of absolute deviations}}{\text{Number of values}} = \frac{16 + 12 + 0 + 5 + 8 + 15}{6} = \frac{56}{6} \approx 9.3
\]

Thus, the mean absolute deviation is approximately **9.3**.