# 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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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 x1, x2, …, xn.

First, find the average or mean of the observations (x_bar) by adding all the observations, and dividing the sum by n: x_bar = (x1 + x2 + … + xn)/n.

Now, calculate the n differences: (x1x_bar), (x2x_bar), …, (xnx_bar).

Then, square those n differences: (x1x_bar)2, (x2x_bar)2, …, (xnx_bar)2.

After that, add these squared differences: (x1x_bar)2 + (x2x_bar)2 + … + (xnx_bar)2.

Later, divide the sum of the squared differences by the number of observations, that is, n, to find the variance (σ2): [(x1x_bar)2 + (x2x_bar)2 + … + (xnx_bar)2]/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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