Question:
The variance of the following frequency distribution is
The variance of the following frequency distribution is
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For grouped frequency distributions, always prepare columns for \(f\), \(fx\), and \(fx^2\). This minimizes calculation mistakes while finding variance.
Updated On: Jun 10, 2026
- \(264\)
- \(88\)
- \(84\)
- \(90\)
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The Correct Option is A
Solution and Explanation
Concept:
For grouped data,
\[
\sigma^2
=
\frac{\sum f_i x_i^2}{N}
-
\left(
\frac{\sum f_i x_i}{N}
\right)^2.
\]
where \(x_i\) are class marks and \(N=\sum f_i\).
Step 1: Determine class marks \[ 5,\;15,\;25,\;35,\;45,\;55. \] \[ N = 2+2+3+4+1+3 = 15. \]
Step 2: Compute \(\sum fx\) \[ \sum fx = 2(5)+2(15)+3(25)+4(35)+1(45)+3(55). \] \[ = 10+30+75+140+45+165. \] \[ =465. \]
Step 3: Compute \(\sum fx^2\) \[ \sum fx^2 = 2(25)+2(225)+3(625)+4(1225)+1(2025)+3(3025). \] \[ = 50+450+1875+4900+2025+9075. \] \[ =18375. \]
Step 4: Calculate variance \[ \sigma^2 = \frac{18375}{15} - \left( \frac{465}{15} \right)^2. \] \[ = 1225-31^2. \] \[ = 1225-961. \] \[ = 264. \] Hence, \[ \boxed{264}. \]
Step 1: Determine class marks \[ 5,\;15,\;25,\;35,\;45,\;55. \] \[ N = 2+2+3+4+1+3 = 15. \]
Step 2: Compute \(\sum fx\) \[ \sum fx = 2(5)+2(15)+3(25)+4(35)+1(45)+3(55). \] \[ = 10+30+75+140+45+165. \] \[ =465. \]
Step 3: Compute \(\sum fx^2\) \[ \sum fx^2 = 2(25)+2(225)+3(625)+4(1225)+1(2025)+3(3025). \] \[ = 50+450+1875+4900+2025+9075. \] \[ =18375. \]
Step 4: Calculate variance \[ \sigma^2 = \frac{18375}{15} - \left( \frac{465}{15} \right)^2. \] \[ = 1225-31^2. \] \[ = 1225-961. \] \[ = 264. \] Hence, \[ \boxed{264}. \]
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