The Standard Deviation is a measure of how spread out numbers are.

This is the formula for Standard Deviation:

\(\displaystyle\sigma={\left(\frac{{1}}{{N}}{\sum_{{{i}-{1}}}^{{N}}}{\left({x}_{{i}}-\mu\right)}^{{2}}\right)}\)

Example:

we have a bunch of numbers like 9, 2, 5, 4, 12, 7, 8, 11.

To calculate the standard deviation of those numbers:

1. Work out the Mean (the simple average of the numbers)

2. Then for each number: subtract the Mean and square the result

3. Then work out the mean of those squared differences.

4. Take the square root of that.

This is the formula for Standard Deviation:

\(\displaystyle\sigma={\left(\frac{{1}}{{N}}{\sum_{{{i}-{1}}}^{{N}}}{\left({x}_{{i}}-\mu\right)}^{{2}}\right)}\)

Example:

we have a bunch of numbers like 9, 2, 5, 4, 12, 7, 8, 11.

To calculate the standard deviation of those numbers:

1. Work out the Mean (the simple average of the numbers)

2. Then for each number: subtract the Mean and square the result

3. Then work out the mean of those squared differences.

4. Take the square root of that.