Standard deviation describes how values are spread around the MeanMean
In Statistics, Mean is the thing you normally know as "average". It's calculated by summing all numbers and then dividing the sum by the number of numbers.
// not the actual way to do it, just po.... Low standard deviation means that the values are tightly clustered around mean (think a spiked graph), while high standard deviation means that the values are spread far apart (think more of like a bell curve).
If you have a group of people with the following heights:
- 160
- 170
- 175
- 180
- 201
The MeanMean
In Statistics, Mean is the thing you normally know as "average". It's calculated by summing all numbers and then dividing the sum by the number of numbers.
// not the actual way to do it, just po... height of the group is (160+170+175+180+201)/5 = 177.2
To calculate standard deviation, we first calculate each height's square deviation (the sqare of it's difference from the mean):
(177.2-160)^2 = 295.84(177.2-170)^2 = 51.84(177.2-175)^2 = 4.84(177.2-180)^2 = 7.84(177.2-201)^2 = 566.44
Next, we calculate Average Variance by averaging all the square deviations: (295.84+51.84+4.84+7.84+566.44)/5 = 185.36
Finally, taking the square root of average variance gives us the standard deviation: sqrt(185.36) = 13.6146979401
If we add 2 people to the group, who are the shortest and tallest persons in the world, our standard deviation would rise to 50.68. If all the people in the group had the same height, standard deviation would be 0.
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