Question:
The mean deviation from the mean for the data $ 6, 7, 10, 12, 13, 4, 12, 16 $ is:
The mean deviation from the mean for the data $ 6, 7, 10, 12, 13, 4, 12, 16 $ is:
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The mean deviation is found by calculating the absolute differences between each data point and the mean, and then averaging them.
Updated On: May 9, 2025
- 3.25
- 3.52
- 3.33
- 2.35
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The Correct Option is A
Solution and Explanation
Step 1: Find the mean of the data.
The mean \( \mu \) is given by:
\[
\mu = \frac{6 + 7 + 10 + 12 + 13 + 4 + 12 + 16}{8} = \frac{80}{8} = 10
\]
Step 2: Find the absolute deviations from the mean.
The absolute deviations are:
\[
|6 - 10| = 4, \quad |7 - 10| = 3, \quad |10 - 10| = 0, \quad |12 - 10| = 2
\]
\[
|13 - 10| = 3, \quad |4 - 10| = 6, \quad |12 - 10| = 2, \quad |16 - 10| = 6
\]
Step 3: Find the mean deviation.
The mean deviation is the average of these absolute deviations:
\[
\text{Mean Deviation} = \frac{4 + 3 + 0 + 2 + 3 + 6 + 2 + 6}{8} = \frac{26}{8} = 3.25
\]
Thus, the mean deviation from the mean is \( \boxed{3.25} \).
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