What is the standard deviation of {1, 2, 3, 4, 5}?

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What is the standard deviation of {1, 2, 3, 4, 5}?

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Answer 1 · 2015-11-01T06:44:50

The answer is $6$ $6$ .

Explanation:

Note that the formula of variance for calculation purpose is

$\frac{1}{n} n \sum i = 1 x_{i}^{2} - {(\frac{1}{n} n \sum i = 1 x_{i})}_{i}^{2}$ $1/n sum_(i=1) ^n x_i^2 - (1/n sum_(i=1)^n x_i)^2$

where $n$ $n$ is the total number of values in the given data set.
In your given data we have $n = 5$ $n = 5$ and the values of $x_{i}$ $x_i$ 's are ${1, 2, 3, 4, 5}$ ${1,2,3,4,5}$ .

So, your variance $= \frac{1}{5} [1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2}] - {(\frac{1}{5} \cdot [1 + 2 + 3 + 4 + 5])}^{2}$ $= 1/5 [ 1^2+2^2+ 3^2 +4^2+5^2] - (1/5 *[ 1+2+3+4+5])^2$
$= 11 - 9$ $= 11 -9$
$= 6$ $=6$

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What is the standard deviation of {1, 2, 3, 4, 5}?

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