MHT CET · Maths · Statistics
The variance, for first six prime numbers greater than 5 , is
- A 27
- B 28
- C 15
- D 20
Answer & Solution
Correct Answer
(B) 28
Step-by-step Solution
Detailed explanation
First six prime numbers greater than 5 are 7,11 , \(13,17,19,23\).
\(\begin{aligned}
& \text { Variance }\left(\sigma^2\right)=\frac{1}{\mathrm{n}}\left(\sum_{\mathrm{i}=1}^{\mathrm{n}} x_{\mathrm{i}}^2\right)-(\bar{x})^2 \\
& \therefore \quad \sigma^2=\frac{1}{6}\left(7^2+11^2+13^2+17^2+19^2+23^2\right) \\
& -\left(\frac{7+11+13+17+19+23}{6}\right)^2 \\
& =\frac{1518}{6}-\left(\frac{90}{6}\right)^2 \\
& =253-225 \\
& =28 \\
&
\end{aligned}\)
\(\begin{aligned}
& \text { Variance }\left(\sigma^2\right)=\frac{1}{\mathrm{n}}\left(\sum_{\mathrm{i}=1}^{\mathrm{n}} x_{\mathrm{i}}^2\right)-(\bar{x})^2 \\
& \therefore \quad \sigma^2=\frac{1}{6}\left(7^2+11^2+13^2+17^2+19^2+23^2\right) \\
& -\left(\frac{7+11+13+17+19+23}{6}\right)^2 \\
& =\frac{1518}{6}-\left(\frac{90}{6}\right)^2 \\
& =253-225 \\
& =28 \\
&
\end{aligned}\)
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