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What is Standard Deviation

Updated on January 31, 2013

Deviation means 'how far from the normal' or to put it another way 'how spread' out are the range of numbers in the sample you are looking at or analysing. This term 'spread out' is also called 'volatility.'

Imagine the numbers were the heights of trees or the heights of people in a school class, so they are all different heights when measured, when you add them all up and divide by how many there are you find out the normal height or 'the Average' or 'the Mean.'

Standard Deviation is then used to tell you how spread out the numbers are.

What is standard deviation used for

Standard deviation is often used on a sample to estimate the value for everybody or for the whole population of what is being measured or estimated. For example using trees if you wanted to know how many trees are in a big big forest you could count them all but this would take forever.

Standard Deviation is widely used, in analysis of people and diseases, in voting, in investment and money, in the stock market, anywhere it is necessary;-

  • to estimate the overall numbers

  • to estimate the level of risk

  • to estimate the level of volatility

Practical Example 1

Using the forest and trees again, if it was time to harvest a section of the forest for trees of particular height research would be conducted and Standard Deviation used as a way to reduce the risk. In this case the statistics would show that there approximately so many trees of the height required in the section planning to be harvested.

A project manager may well ask for research in a number of sections to pick the best, that is the one where the Standard Deviation has the least volatility.

So What

People working with trees need information like this to allow them to classify the trees, to reduce the risk of cutting the wrong place. You will often see a table of data that started off with someone calculating the Standard Deviation.

You could measure all the trees one by one but that would be tedious and boring..

What a scientist or statistician will do is select a sample and then use Standard Deviation to estimate the numbers for the entire forest. This is an important and accepted scientific method of figuring out the characteristics of a large group or population of things when it is almost impossible to count them all.

Tree Population in Section XYZ

Tree Type
Height Range
No. Per Acre
Est. Diameter
23 inches
17 inches
9 inches

For example if samples were taken and all the trees were divided into Large, Medium and Small their characteristics could then be estimated

  • their height range,

  • the number per hectare or acre

  • their estimated diameter.

These estimates are calculated using Standard deviation and from these will come projected or anticipated timber yields when they are about to be harvested.


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    • Drax profile image

      des donnelly 5 years ago from NYC....

      DW... I've made my living with Excel and analysing stats for years, it is as much pleasure as anything to work with a decent set of complex numbers. They are like an old foreign comrade, after a time you understand the unspoken, the nuances...



    • profile image

      win-winresources 5 years ago from Colorado


      Don't be threatened by statistics like standard deviation. Its just simple math. But what it represents is a powerful tool that will help you make better decisions and develop better understandings.

      Good luck.


    • Drax profile image

      des donnelly 5 years ago from NYC....

      thanks for the comment Doc.. I was looking at your Ch4 there and it is very comprehensive, I must go back and read it in detail and the others. I am away to the attic now to look for my slide rule... ;-) just joking... !!

    • profile image

      win-winresources 5 years ago from Colorado


      I wrote Statistics Made Easy - Really here on hubpages about 2 months ago. Chapter 4 is the one dealing with the Measures of Dispersion in which Standard Deviation resides.

      Simply put, a standard deviation is the difference between a score (or observation) from the mean of all of the scores (or observations). It reflects the variability of all of the scores about the mean. It is the square root of the variance.