Question

PLEASE HELP!!!

For the data set 7, 5, 10, 11, 12, the mean, x, is 9. What is the standard
deviation?

Answer 1

The answer I believe would be 2.9 deviation

Answer 2

Answer: B) 2.9 approximately

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Step-by-step explanation:

The weird or fancy looking E symbol is the greek uppercase letter sigma. It is effectively the english version of S to represent summation. So we add up all the
`(x-\overline{x})^2` terms to get this. Luckily this has already been done for us in the table where they wrote "sum = 34", so
`\sum(x-\overline{x})^2 = 34`

From here, we substitute this into the formula, along with n = 5 since there are 5 items in the original list

So,

`s = \sqrt{(1)/(n-1)\sum(x-\overline{x})^2} \\\\s = \sqrt{(1)/(5-1)*34} \\\\s = \sqrt{(1)/(4)*34} \\\\s = √(0.25*34) \\\\s = √(8.5) \\\\s \approx 2.91547594742266 \\\\s \approx 2.9 \\\\`

This computes the sample standard deviation. To get the population standard deviation, you'd basically change the "n-1" to simply "n", and the rest of the formula is identical.