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Asked Sep 11, 2019

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how do you find standard deviation? how many bars should you have for a standard deviation? do you necessarily have to find variance or mean before you find standard deviation?

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Step 1

**Introduction:**

The standard deviation of a set of observations is the square root of the average of the sum of squared deviations from the mean of those observations.

Step 2

**How to find:**

Let there be *n* observations, denoted by *x*_{1}, *x*_{2}, …, *x _{n}*.

First, find the average or mean of the observations (*x*_bar) by adding all the observations, and dividing the sum by *n*: *x*_bar = (*x*_{1} + *x*_{2} + … + *x _{n}*)/

Now, calculate the *n* differences: (*x*_{1} – *x*_bar), (*x*_{2} – *x*_bar), …, (*x _{n}* –

Then, square those *n* differences: (*x*_{1} – *x*_bar)^{2}, (*x*_{2} – *x*_bar)^{2}, …, (*x _{n}* –

After that, add these squared differences: (*x*_{1} – *x*_bar)^{2} + (*x*_{2} – *x*_bar)^{2} + … + (*x _{n}* –

Later, divide the sum of the squared differences by the number of observations, that is, *n*, to find the variance (*σ*^{2}): [(*x*_{1} – *x*_bar)^{2} + (*x*_{2} – *x*_bar)^{2} + … + (*x _{n}* –

Finally, find the positive square root of the average of the sum of squared deviations from the mean to find the standard deviation, (*σ*).

The formula is given as follows:

Step 3

**Discussion:**

The standard deviation is one of the quantities that is useful for creating “error bars”, which are usually represented as one standard deviation, one standard error, etc....

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