Question:
The variance of 240, 260, 270, 280 is ________.
The variance of 240, 260, 270, 280 is ________.
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Subtract a common constant to simplify calculations; variance remains unchanged.
Updated On: Jun 26, 2026
- $\frac{475}{4}$
- $\frac{475}{2}$
- $\frac{475}{8}$
- $\frac{475}{16}$
- $\frac{875}{4}$
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The Correct Option is
Solution and Explanation
Step 1: Concept
Mean $\bar{x} = (240+260+270+280)/4 = 1050/4 = 262.5$.
Step 2: Meaning
Variance $\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}$.
Step 3: Analysis
Differences: $(22.5)^2, (2.5)^2, (7.5)^2, (17.5)^2$. Summing squares: $506.25 + 6.25 + 56.25 + 306.25 = 875$.
Step 4: Conclusion
Variance $= 875/4$. Final Answer: (E)
Mean $\bar{x} = (240+260+270+280)/4 = 1050/4 = 262.5$.
Step 2: Meaning
Variance $\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}$.
Step 3: Analysis
Differences: $(22.5)^2, (2.5)^2, (7.5)^2, (17.5)^2$. Summing squares: $506.25 + 6.25 + 56.25 + 306.25 = 875$.
Step 4: Conclusion
Variance $= 875/4$. Final Answer: (E)
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