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)

Ο 56

11.2

150

9.3

Answer 1

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

1. **Calculate the Mean:**
\[
\text{Mean} = \frac{\sum \text{data points}}{n} = \frac{134 + 138 + 150 + 155 + 158 + 165}{6}
\]
\[
= \frac{1000}{6} \approx 166.67
\]

2. **Calculate the Absolute Deviations:**
- \( |134 - 150| = 16 \)
- \( |138 - 150| = 12 \)
- \( |150 - 150| = 0 \)
- \( |155 - 150| = 5 \)
- \( |158 - 150| = 8 \)
- \( |165 - 150| = 15 \)

3. **Calculate the Mean of the Absolute Deviations:**
\[
\text{MAD} = \frac{\sum |x_i - \text{Mean}|}{n} = \frac{16 + 12 + 0 + 5 + 8 + 15}{6} = \frac{56}{6} \approx 9.33
\]

4. **Round to the Nearest Tenth:**
\[
\text{Rounded MAD} \approx 9.3
\]

Thus, the mean absolute deviation of the dataset is **9.3**.