Q75 / 160 · TS EAMCET 2020 (11 Sep Shift 1) · Mathematics
The variance of the following frequency distribution is
- A165.3
- Correct answerB161.1
- C282.1
- D152.5
Solution
Given frequency distribution
$\because \quad N=\Sigma f_i=70$ $\therefore$ variance $\left(\sigma^2\right)=\frac{1}{N} \Sigma f_i x_i^2-\left[\frac{1}{N} \Sigma f_i \cdot x_i\right]^2$ $=\frac{1}{70}(42150)-\left[\frac{1}{70}(1470)\right]^2=\frac{4215}{7}-441$ $=\frac{4215-3087}{7}=\frac{1128}{7}=161.1$
$\because \quad N=\Sigma f_i=70$ $\therefore$ variance $\left(\sigma^2\right)=\frac{1}{N} \Sigma f_i x_i^2-\left[\frac{1}{N} \Sigma f_i \cdot x_i\right]^2$ $=\frac{1}{70}(42150)-\left[\frac{1}{70}(1470)\right]^2=\frac{4215}{7}-441$ $=\frac{4215-3087}{7}=\frac{1128}{7}=161.1$
Hence, the correct answer is option: 'B'.