Question:
The mean deviation about the mean from the data 400, 410, 420, 430, 440 is:
The mean deviation about the mean from the data 400, 410, 420, 430, 440 is:
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The mean of an arithmetic progression is always the middle term if the number of terms is odd.
Updated On: Apr 28, 2026
- 14
- 10
- 20
- 12
- 16
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Find the mean $(\bar{x})$, then find the average of the absolute differences $|x_i - \bar{x}|$.
Step 2: Analysis
$\bar{x} = \frac{400 + 410 + 420 + 430 + 440}{5} = \frac{2100}{5} = 420$. Differences from 420: $|400-420|=20, |410-420|=10, |420-420|=0, |430-420|=10, |440-420|=20$.
Step 3: Calculation
Mean Deviation $= \frac{20 + 10 + 0 + 10 + 20}{5} = \frac{60}{5} = 12$. Final Answer: (D)
Find the mean $(\bar{x})$, then find the average of the absolute differences $|x_i - \bar{x}|$.
Step 2: Analysis
$\bar{x} = \frac{400 + 410 + 420 + 430 + 440}{5} = \frac{2100}{5} = 420$. Differences from 420: $|400-420|=20, |410-420|=10, |420-420|=0, |430-420|=10, |440-420|=20$.
Step 3: Calculation
Mean Deviation $= \frac{20 + 10 + 0 + 10 + 20}{5} = \frac{60}{5} = 12$. Final Answer: (D)
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