1. Tardigrade
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  4. For the data 30,31,32, ldots, 45,46. Evaluate variance.

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Q. For the data $30,31,32, \ldots, 45,46$. Evaluate variance.

Statistics

Solution:

Mean $\Rightarrow \frac{30+31+32+\ldots+45+46}{17}$
$=\frac{\frac{17}{2}(30+46)}{17}$
$\Rightarrow \bar{x}=38$
$\Rightarrow$ Variance $=\frac{1}{n} \Sigma(x-\bar{x})^{2}$
$=\frac{1}{17}\left(8^{2}\right.+7^{2}+6^{2}+\ldots \left.+1^{2}+0^{2}+1^{2}+2^{2}+\ldots+3^{2}\right)$
$=\frac{1}{17} \times 2\left(1^{2}+2^{2}+\ldots+8^{2}\right)$
$=\frac{2}{17} \times \frac{8(8+1) \cdot(2 \times 8+1)}{6}$
$=\frac{2}{17} \times \frac{8 \times 9 \times 17}{6}=24$