Can you find the standard deviation of negative numbers?

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Can you find the standard deviation of negative numbers?

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Answer 1 · 2015-11-01T16:26:13

Yes.

Explanation:

Yes. Why not?!!

Consider the data sets ${- 1, - 2, - 3, - 4, - 5}$ ${-1,-2,-3,-4,-5}$ . Note that all are negative numbers.

So, variance of the data set will be $\frac{1}{n} n \sum i = 1 x_{i}^{2} - {(\frac{1}{n} n \sum i = 1 x_{i})}_{i}^{2}$ $1/n sum_(i=1) ^n x_i^2 - (1/n sum_(i=1)^n x_i)^2$
$= \frac{1}{5} [{(- 1)}^{2} + {(- 2)}^{2} + {(- 3)}^{2} + {(- 4)}^{2} + {(- 5)}^{2}] - {(\frac{1}{5} \cdot [- 1 - 2 - 3 - 4 - 5])}^{2}$ $= 1/5 [ (-1)^2+(-2)^2+ (-3)^2 +(-4)^2+(-5)^2] - (1/5 *[ -1-2-3-4-5])^2$
$= 11 - 9$ $= 11 -9$
$= 6$ $=6$

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Can you find the standard deviation of negative numbers?

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