Question:
The variance for the data: $65, 70, 75$ is
The variance for the data: $65, 70, 75$ is
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Variance measures spread: square deviations, then take average.
Updated On: Apr 24, 2026
- $\frac{50}{3}$
- $\frac{55}{3}$
- $\frac{50}{6}$
- $\frac{50}{2}$
- $70$
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The Correct Option is A
Solution and Explanation
Concept:
• Variance: $\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}$
Step 1: Find mean
\[ \bar{x} = \frac{65 + 70 + 75}{3} = 70 \]
Step 2: Find deviations
\[ 65-70 = -5,\quad 70-70 = 0,\quad 75-70 = 5 \]
Step 3: Square deviations
\[ 25,\;0,\;25 \]
Step 4: Compute variance
\[ \sigma^2 = \frac{25+0+25}{3} = \frac{50}{3} \] Final Conclusion:
\[ = \frac{50}{3} \]
• Variance: $\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}$
Step 1: Find mean
\[ \bar{x} = \frac{65 + 70 + 75}{3} = 70 \]
Step 2: Find deviations
\[ 65-70 = -5,\quad 70-70 = 0,\quad 75-70 = 5 \]
Step 3: Square deviations
\[ 25,\;0,\;25 \]
Step 4: Compute variance
\[ \sigma^2 = \frac{25+0+25}{3} = \frac{50}{3} \] Final Conclusion:
\[ = \frac{50}{3} \]
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