# How to Calculate Standard Deviation

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**How to Calculate Standard Deviation**

Standard Deviation, often calculated along with the mean of a data set, tells us how spread out the data is. It is used for data that is normally distributed and can be easily calculated using a graphing calculator or spreadsheet software, but it can also be calculated with a few math operations.

To calculate the standard deviation, the first step is to calculate the mean of the data set, denoted by x with a line over it, also called x-bar.

Video by Jeremy Jones

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how to calculate standard deviation how

many vegetables do you have in your

fridge is that a common amount or are

you an outlier we can use standard

deviation to know whether someone’s

behavior is normal or extraordinary

standard deviation often calculated

along with the mean of a data set tells

us how spread out the data is it is used

for data that is normally distributed

and can be easily calculated using a

graphing calculator or spreadsheet

software but it can also be calculated

with a few math operations we’re going

to use an example involving the number

of vegetables five of our friends have

in their fridges they have two three

four seven and nine vegetables we

calculate the standard deviation the

first step is to calculate the mean of

the data set denoted by X with a line

over it also called x-bar in this case

the mean would be 2 plus 3 plus 4 plus 7

plus 9 divided by 5 which equals 5

our average friend has five vegetables

in their fridge the second step is to

subtract the mean from each data point

to find the differences it’s helpful to

use a table like this 2 minus 5 equals

negative 3 3 minus 5 equals negative 2 4

minus 5 equals negative 1 7 minus 5

equals 2 and 9 minus 5 equals 4 the

third step is to square each difference

this makes all the difference is

positive so they don’t cancel each other

out and it also magnifies larger

differences and minimizes smaller

differences negative 3 squared equals 9

negative 2 squared equals 4 negative 1

squared equals 1 2 squared equals 4 and

4 squared equals 16 the fourth step is

to calculate the mean of the squared

differences 9 plus 4 plus 1 plus 4 plus

16 divided by 5 equals 6 point 8

the final step is to take the square

root this counteracts the squaring we

did earlier and allows the standard

deviation to be expressed in the

original units the square root of 6.8 is

about 2.6 and that’s the standard

deviation we’re done the mean number of

vegetables is five with a standard

deviation of two point six veggies

knowing that about two-thirds of the

data fall within one standard deviation

of the mean assuming the data is

normally distributed we can say that

about two-thirds of our friends have

between two point four and seven point

six vegetables in their fridges to recap

these are the five steps for calculating

standard deviation calculate the mean

subtract the mean from each data point

square each difference calculate the

mean of the squared differences and take

the square root using symbols the

equation for calculating standard

deviation looks like this lowercase

Sigma stands for standard deviation of a

population upper case Sigma tells us to

calculate the sum for each instance X is

each data point x-bar is the mean of the

data points and n is the number of data

points keep in mind that there is a

similar formula that divides by n minus

1 that formula is used when you only

have data for a sample of the population

hope this was helpful see you next time

you.

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