The standard deviation of first 10 multiples of 4 is

The standard deviation of first 10 multiples of 4 is
  1. $7$
  2. $8$
  3. $11.5$
  4. $14$

Solution

Entries are $4,8,12,16,20,24,28,32,36,40$. $ \begin{aligned} \text { Variance } & =\frac{\sum_{i=1}^{10}(4 i)^2}{10}-\left(\frac{\sum_{i=1}^{10} 4 i}{10}\right)^2 \\ & =\frac{16 \times 10 \times 11 \times 21}{60}-\left(\frac{4 \times 55}{10}\right)^2 \\ & =132 \end{aligned} $ $\therefore$ Standard deviation $=\sqrt{132} \approx 11.5$

Asked in: AP EAMCET 2022 (07 Jul Shift 2)

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