Learn about standard deviation and variance, which we use to measure how tightly or loosely clustered the data is around the mean.
Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)
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The variance σ2 of a dataset measures the spread of data around the mean.
The standard deviation σ is the square root of the variance. The advantage of the standard deviation is that is has the same units as the original data.
When you use a calculator to find standard deviation:
Enter your data into L1 using STAT > EDIT. Then, use STAT > CALC > 1-Var Stats and enter L1 as your list by clicking 2ND then 1.
You will see two values: Sx and σx. We use Sx when the data is a sample of a large population, and σx when the data represents the entire population. The difference is due to the fact that a sample will usually have a smaller variance than the population, because there are fewer elements.
If we have a dataset with mean xˉ and standard deviation σ, then if we
add a constant +b to the dataset, the mean increases by b and the standard deviation does not change
scale the values by a, then both the mean and the standard deviation are scaled by a.