Question

What is the standard deviation?

Mean: 34
14, 14, 20, 38, 47, 48, 57

Answer 1

`$\sigma={\sqrt {\frac {529+196+169+16+196+400+400}{7}}}$`The formula for calculating standard deviation is
`\sigma={\sqrt {\frac {\sum(x_(i)-{\mu})^(2)}{n}}}`, where

`\sigma` is the population standard deviation,
`n` is the population size,
`x_(i)` is each value from the population, and
`\mu` is the population mean. We can substitute each value into the formula and simplify, which gives us our standard deviation.

`$\sigma={\sqrt {\frac {(57-34)^(2)+(48-34)^(2)+(47-34)^(2)+(38-34)^(2)+(20-34)^(2)+(14-34)^(2)+(14-34)^(2)}{7}}}$`

`$\sigma={\sqrt {\frac {(23)^(2)+(14)^(2)+(13)^(2)+(4)^(2)+(-14)^(2)+(-20)^(2)+(-20)^(2)}{7}}}$`

`$\sigma={\sqrt {\frac {529+196+169+16+196+400+400}{7}}}$`

`$\sigma={\sqrt {\frac {1906}{7}}}$`

`$\sigma = √(272.285714286)$`

`$\sigma \approx 16.5010822156$`

Our answer is
`$\sigma \approx 16.5010822156$`, or, for convenience,
`$\sigma \approx 16.501082$`, which is the most digits you'll probably need for any calculations you make.

Hope this helps!