Learn about standard deviation and variance, which we use to measure how tightly or loosely clustered the data is around the mean.
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Practice exam-style standard deviation and variance problems
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.