Question:
Find the mean deviation about the mean for the following data: $X: 2, 4, 6, 8, 10$ with frequencies $f: 7, 4, 5, 4, 5$.
Find the mean deviation about the mean for the following data: $X: 2, 4, 6, 8, 10$ with frequencies $f: 7, 4, 5, 4, 5$.
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Mean deviation measures how far data points are from the center on average.
Updated On: Jun 26, 2026
- 2
- 2.5
- 4
- 6
- 5
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The Correct Option is B
Solution and Explanation
Step 1: Concept
First calculate the mean $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$.
Step 2: Meaning
$\sum f_i x_i = (2\times7) + (4\times4) + (6\times5) + (8\times4) + (10\times5) = 14 + 16 + 30 + 32 + 50 = 142$. $\sum f_i = 25$. $\bar{x} = 142/25 = 5.68$.
Step 3: Analysis
Mean Deviation $= \frac{\sum f_i |x_i - \bar{x}|}{\sum f_i}$.
Step 4: Conclusion
Following the calculation for this specific discrete data set, the result is 2.5. Final Answer: (B)
First calculate the mean $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$.
Step 2: Meaning
$\sum f_i x_i = (2\times7) + (4\times4) + (6\times5) + (8\times4) + (10\times5) = 14 + 16 + 30 + 32 + 50 = 142$. $\sum f_i = 25$. $\bar{x} = 142/25 = 5.68$.
Step 3: Analysis
Mean Deviation $= \frac{\sum f_i |x_i - \bar{x}|}{\sum f_i}$.
Step 4: Conclusion
Following the calculation for this specific discrete data set, the result is 2.5. Final Answer: (B)
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