# How to remember the standard deviation

The standard deviation formula is:

Standard deviation `=sigma=sqrt((Sigma(x-bar x)^2)/(n-1))`

1. Find the mean (of all the numbers) `= barx`

2. Subtract the mean (from each number) `= x-barx`

3. Square the result (of each of the above) `= (x-barx)^2`

4. Add the results up (Add) `=sum(x-barx)^2`

5. Divide (the result) by the number of data values minus one `=(sum(x-barx)^2)/(n-1)`

6. Take the square root of the result `=sqrt((sum(x-barx)^2)/(n-1))`

The following story should help you remember all of the above.

To set the standards |
Standard | |

Any deviants |
Deviation | |

Standard deviation `=sigma`

and these **mean **ones are **taken out** of the class `=x-barx`

`Each\ \n\u\m\b\er - mean`

they are all put in the school **square** `=s\q\u\a\r\e`

`(Each\ \n\u\m\b\er - mean)^2`

then there is a roll call to** add** up the deviants `=ADD`

`sum(Each\ \n\u\m\b\er - mean)^2`

then they have to run **over n**inety miles `=\ \/n`

`(sum(Each\ \n\u\m\b\er - mean)^2)/n`

there is always **one** that doesn't make it back `=-1`

`(sum(Each\ \n\u\m\b\er - mean)^2)/(n-1)`

This **roots** out any problems

`sqrt((sum(Each\ \n\u\m\b\er - mean)^2)/(n-1))`

So

Standard deviation `=sigma=sqrt((sum(x-barx)^2)/(n-1))`

In more detail and with pictures you would remember this as follows:

To set the standards any deviants have a whistle blown at them.

A whistle and sigma look very alike.

Subtract the mean.

Then square each result.

All these** mean** ones are then marched into the school **square**.

Add all the results.

There is a roll call to **add** up all the deviants.

**NOTE: **

If you just learnt up to this point this would help you enormously with how to work out what the equation means.

The deviants are made to run **over** (÷) **n**inety (n) miles.

There is always one that doesn’t make it back (-1).

Square root the result.

This** roots** out any problems (√).