JEE MAIN - Mathematics (2023 - 31st January Morning Shift - No. 23)
If the variance of the frequency distribution
| $$x_i$$ | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|
| Frequency $$f_i$$ | 3 | 6 | 16 | $$\alpha$$ | 9 | 5 | 6 |
is 3, then $$\alpha$$ is equal to _____________.
Answer
5
Explanation
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$\sigma_{\mathrm{x}}^{2}=\sigma_{\mathrm{d}}^{2}=\frac{\sum \mathrm{f}_{\mathrm{i}} \mathrm{d}_{\mathrm{i}}^{2}}{\sum \mathrm{f}_{\mathrm{i}}}-\left(\frac{\sum \mathrm{f}_{\mathrm{i}} \mathrm{d}_{\mathrm{i}}}{\sum \mathrm{f}_{\mathrm{i}}}\right)^{2}$
$=\frac{150}{45+\alpha}-0=3$
$\Rightarrow 150=135+3 \alpha$
$\Rightarrow 3 \alpha=15 \Rightarrow \alpha=5$
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