How to Calculate Standard Deviation
How to do standard deviation, listing the 6 simple steps required, 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 ;-
1. Get the Mean
2. Get the deviations
3. Square these
4. Add the squares
5. Divide by total numbers less one
6. Square root of result is Standard Deviation
SO STEP BY STEP;-
1. get the Mean
to begin you need the mean or the average, for example add 23, 92, 46, 55, 63, 94, 77, 38, 84, 26 ... = 598 divide by 10 (the actual number of numbers) 598 divided by 10 = 59.8
so the mean or average of 23, 92, 46, 55, 63, 94, 77, 38, 84, 26 is
2. 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
3. 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
4. add the squares
total of these numbers is 6,283.60
5. 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
6. square root of result is Standard Deviation
square root is the number multiplied by itself to get 698.18 which is:-
26.4 so 26.4 is the Standard Deviation...
Ok so above is the manual method of doing this
Step by step example using Excel...
Calculating standard deviation using Excel
- view or download spreadsheet
Standard deviation example spreadsheet in Google docs, click on file click on download and save the excel spreadsheet
Enter your range of numbers as shown in cells 1 to 10..
Step 1 - Photo 1
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
Step 2 - Photo 2
Just hit enter
The Mean or Average will now appear in Cell 11
Step 2a - Photo 2a
same as before 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 3 - Photo 3
The Standard Deviation will now appear in Cell 12
Step 4 - Photo 4
Pat yourself on the back if...
your final calc matches this...
and the Final Score is...26.4
Here is the link to the excel sheet, you can simply download it as an excel sheet and modify it to your needs.... :-)
- standard deviation_v1.xls - Google Docs
Standard deviation example spreadsheet in excel, just click on File and Download and save as excel spreadsheet
What Does Standard Deviation Tell You
Standard deviation is all about dispersion - how the set of numbers or data you have deviate 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, teams performances, motorsport, horse racing
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 calc has hub scores from 23 to 94 in other words there is a lot of volatility...
So if one wished to rank hubpages it may 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
More Probability & Statistical Hubs by Drax
- What is Standard Deviation
- How to Use the Excel Descriptive Statistics tool
Use the Excel Descriptive Statistics tool to quickly calculate the Mean, Standard Error, Median, Mode, Standard Deviation, Sample Variance, Kurtosis, Skewness, Range, Minimum, Maximum, Sum, Count, Largest(1), Smallest(1), Confidence Level(95.0%)