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What is Standard Deviation
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.
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
No. Per Acre
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.
More Probability & Statistical Hubs by Drax
- How to Calculate Standard Deviation
This is a hubpages article which describes how to Calculate Standard Deviation manually in six straightforward steps;- 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 resu
- How to Use the Excel Descriptive Statistics tool