Standard Deviation Formulas | Excel
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Standard deviation is basically defined as an amount or quantity that would be calculated to show the extent of deviation for a set or group as one whole.
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Standard deviations are used most by those who will deal with statistics in any way. If we were to look at this subject at the simplest possible level, standard deviations would be a number, after calculation, that would represent the similarity in a set of numbers. Means simply put would be averages.
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Whilst it is not necessary to learn the formula for calculating the standard deviation, there may be times when you wish to include it in a report or dissertation.
The standard deviation of an entire population is known as σ (sigma) and is calculated using: |
Where x represents each value in the population, μ is the mean value of the population, Σ is the summation (or total), and N is the number of values in the population.
The standard deviation of a sample is known as S and is calculated using: |
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Example
If you take for example a group of Boy Scouts who are all the same age. Many of the boys in this age group would be around the same height. If age were to dictate that boys were usually or normally 5 ft 1 in, it would be likely that wouldn’t be much difference or, little deviation in the height of the Boy Scouts in that age group.
In another example if you went into a beauty salon and averaged how many women would come in the door with short hair, shoulder length hair and how many were just coming in with exceptionally long hair just to trim the dead ends. Averaging those numbers would likely show a lot of differentiation because it’s likely that there would be plenty of differentiation in the length of the group for the day, in the length of their hair.
Let’s look at a restaurant that had decided to survey a group of 100 of their customers for a day at the end of their meals. Say we would ask them if they liked the food and would come back again to dine in their restaurant or if they were not impressed and said they would never come back again.
If 50 of those customers said they loved the food and would come back again and 50 customers said that they didn’t like the food and would never come back again, there would be a lot of differentiation. A lot of people are in disagreement. One half of the customers are saying yes to the survey and half are saying no. This very clear disagreement shows a very large lack in consensus or…a large standard deviation. If this were the case, it would be very difficult for the owners to decide how to effectively change the menu when so many people disagree.
However, if 90 of those customers said that they absolutely loved the restaurant and would definitely return and 10 people said it was “ok” and would probably come back again then the customers, in general, agree that the restaurant would be a place that they would be willing to at least consider coming back to. All in all they intend to return at some point. This will show that there is very little differentiation. There is hardly any disagreement at all. The point is, it shows a very small or narrow standard deviation.
Bottom line
If you have a small standard deviation you have a lot of agreement in opinions. If you have a large standard deviation you have many opinions that do not agree.
If you would like to see some easy but more technical examples, see the information contained in links above. Keep it simple in your mind as you begin the journey into placing standard deviations into numbers.
Sources
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