# How to Calculate Standard Deviation

In this article, I will show you how to do the standard deviation, listing the 6 simple steps required, and showing the process manually and also describing how to do it using Excel (includes links to a downloadable spreadsheet of the examples given).

## Six Straightforward Steps on How to Calculate Standard Deviation

- Get the mean
- Get the deviations
- Square these
- Add the squares
- Divide by total numbers less one
- Square root of the result is the standard deviation

## Step-By-Step Example

Here is a step-by-step example of how to do the standard deviation with the manual method.

**Get the mean:**To begin with, you need to find the mean or the average. For example, add 23, 92, 46, 55, 63, 94, 77, 38, 84, 26 = 598, then divide by 10 (the actual number of numbers) which is 598 divided by 10 = 59.8. So the mean or average of 23, 92, 46, 55, 63, 94, 77, 38, 84, 26 is**59.8****Get the deviations:**Subtract the mean from each of the numbers. The answers are: -36.8, 32.2, -13.8, -4.8, 3.2, 34.2, 17.2, -21.8, 24.2, -33.8**Square These:**To square means multiply them by themselves. The answers are: 1354.24, 1036.84, 190.44, 23.04, 10.24, 1169.64, 295.84, 475.24, 585.64, 1142.44**Add the squares:**The total of these numbers is 6,283.60**Divide by total number of numbers less one:**You had 10 numbers less 1 is 9 numbers, so 6283.60 divided by 9 = 698.18**The Square root of the result is the standard deviation:**A square root is the number multiplied by itself to get 698.18 which is 26.4, so**26.4 is the standard deviation.**

## Step-By-Step Example Using Excel

Now I will show you how to calculate the standard deviation using Excel. You will need to download the spreadsheet file below or make your own in order to do this.

- view or download spreadsheet

Standard deviation example spreadsheet in Google docs, click on file click on download and save the excel spreadsheet

## Step 1

Enter your range of numbers as shown in cells 1 to 10.

## Step 2

- Place the cursor in Cell 11.

- Go to the menu bar, select insert, select function: the insert function dialog box opens.

- Click on the category and select Statistical.

- In the window below select Average.

- Hit enter.

## Step 2a

- When you hit enter another dialog box will appear asking you to confirm the range, i.e. the numbers in cells 1 to 10 that you wish to perform the calculation on.

- Just hit enter.

- The Mean or Average will now appear in Cell 11.

## Step 3

- Place the cursor in Cell 12.
- Go to the menu bar, select insert, select function.
- The function dialog box will open, select statistical, in the window below scroll down and select STDEV.

## Step 4

- When you hit enter another dialog box will appear asking you to confirm the range, i.e., the numbers in cells 1 to 10 that you wish to perform the calculation on. Since it automatically seeks to perform the calc on all the cells above you will have to change the range from D4:D14 to D4:D13.

- The standard deviation will now appear in Cell 12.

## Pat Yourself on the Back If

Your final calculation matches the image below.

## What Does the Standard Deviation Tell You

The standard deviation is all about dispersion, how the set of numbers or data you have deviates from the mean; this is essentially a measure of uncertainty.

**Low Deviation**shows the numbers are all reasonably similar**High Deviation**shows there is a lot of fluctuation in the numbers.

### How can you use it:

- Conducting investment research since this is an aid to measuring or calculating volatility.
- Making weather comparison between locations or year to year.
- Analysing agricultural yields and/or prices.
- Almost everything to do with population analysis.
- Lots of things in sports, with athletes, team performances, motorsports, horse racing, etc.

**All these analyses help in prediction by looking closely at past performance.**

## Example: Using Deviation to Analyse Hub Scores

Just say we were using deviation to analyse hub scores, in the example below all the hub scores, are above 90, when the SD is calculated for this range the SD is 2.92. This is low; as a contrast the original calculation has hub scores from 23 to 94; in other words, there is a lot of volatility.

So if one wished to rank HubPages, it might be that those with a lower standard deviation, i.e., less volatility are more consistent, and so we enter the esoteric world of statistics. Imagine this was horses.

## An Example of Using SD

## Questions & Answers

**© 2006 des donnelly**

## Comments

I will surely visit back for more –Great job!

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Thanks for this, I missed this in class, your explanation is probably a lot easier to understand anyways!

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Very informative and nicely explained. Well done!

I teach standard deviation once every 2 months, and the excel stuff was nice. Good idea to add some poetry :)

Great and helpful! I took Algebra I and II, Geometry, Trig, and Honors Pre-Cal in high school as well as college classes, but never took Prob and Stats! This hub is easy to follow and I can use it to help my kids in the classroom!

Thanks very thanks sir

Thanks. This really helped me help my daughter with her maths homework.

Thank you so much for your simple breakdown on how to calculate a Standard Deviation both manually and using Excell. It was straight to the point and the example was quite helpful. I will now be able to help my sister understand the concept also.

THANK YOU!!! :-)

thanks and nice post

Very useful hub..Thanks alot.

That is one of the clearest expositions of the methods of calculating standard deviation that I have ever seen. really, some tutors do seem to make these things unnecessarily complicated.

Most mathematical and statistical procedures are only complex in their sum but each step is simple in itself. Your hub amply and ably demonstrates this principle.

absolutely brilliant!!

thanks for the hard work

saved me heaps of time =)

fantastic those steps has enabled me to understand how to calculate standard deviation.

very well done

this is a really hlpful page and its very much appreciated that you take the time to explain how to figure out standard deviation, although i have to say that when you say you divide the total number less one. i find that my answers are never correct. they are only correct when i divide by the total numbers. the equations in my foundation math book also say that it is divide by total numbers. it says nothing about divide less one. other than that this page helps keep me on track until i have it memorized. so thank you

this is very helpful for me, except it doesn't work when you divide by the number less one.... you need to divide by the number to get the correct answer

this helped me in my statistics exam

Very helpful information! Thanks for writing. I Googled help to find this and found a fellow hubber as the top result! Great to know that we can make it up there. Look forward to stumbling upon you again!

This is by far the most helpful and strait forward explanation I have ever seen. THANKS!

Hi Drax, thanks for giving stepwise information about SD

Hey Drax, thanks for the info. A complex topic made easy. voted up!

I remember everyone struggling with this when I did my Psychology stats - great posting!

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Thanks soo much..timely help

Greatings from Norway:-)

thnks drax i really needed this for hw i did this before but didn't understand now i do.

thanks

kimberly

thanks u make my efforts easy

the description is so simple....thank u so much

thanks for all the help. It helped me a TON!

this is great, thanx for making it easy

This is Awesome!!!!!

Thanks a lot :) Very helpful step by step for my research assignment!

veryyyy veryyyy veryyy helpful. thanks :)

Awesome example on standard deviation. Very helpful.

I think it's better

Thats was fantastic. I think this is all I needed and really helped moi. Thanks man!!

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hey how to calculate the standard error of xy plot????

You made it really simple for me buddy!! Thanks!

Great, simple quidance, but isn't this the formula for the unbiased estimate of the population variance, rather than the standard deviation which only consideres the sample given?

Difference between these two would be in step 5, for standard deviation one does not need to substract 1 from the divisor. :)

why we use standard deviation means what is the application of standard deviation..

very good way to learn something. easy way for understanding.

Such a wonderful presentation!!!!!!!!!!!!!!! Thanks dude

hi, i am really learning and i am enjoying your piece of work i hope i understand these better. since it is simplified for those who are slow learners!!!!!!!!! thanks a lot.

very usefull...easy to understand..thanks

What if you have a missing data, how do you find it if you have a standard deviation of 3?

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i absolutely love this after 20 yrs out of school i was unable to have this make sense wow thank you so much!! :)0

really well and clearly explained, thank you so much! brilliant help to me this was!

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