Variance and Standard Deviation: Statistics

Greetings math friends! In this post we’re going to go over variance and standard deviation. We will take this step by step to and explain the significance each have when it comes to a set of data. Get your calculators ready because this step by step although not hard, will take some serious number crunching! Check out the video below to see how to check your work using a calculator and happy calculating! 🙂

What is the Variance?

The variance represents the spread of data or distance each data point is from the mean.  When we have multiple observations in our data, we want to know how far each unit of data is from the mean.  Are all the data points close together or spread far apart?  This is what the variance tells us!

Don’t freak out but here’s the formula for variance, notated as sigma squared:

Variance and Standard Deviation

This translates to:

variance formula

Let’s try an example:

variance formula
Variance and Standard Deviation
Variance and Standard Deviation
Variance and Standard Deviation
Variance and Standard Deviation
Variance and Standard Deviation

What is Standard Deviation?

Standard deviation is a unit of measurement that is unique to each data set and is used to measure the spread of data. The formula for standard deviation happens to be very similar to the variance formula!

Below is the formula for standard deviation, notated as sigma:

sample standard deviation

Since this is the same exact formula as variance with a square root, all we need to do is take the square root of the variance to find standard deviation:

sample standard deviation

Now try calculating these statistics on your own with the following practice problems!

Practice Questions:

sample standard deviation

Solutions:

sample standard deviation

Still got questions? No problem! Don’t hesitate to comment with any questions or check out the video above. Happy calculating! 🙂

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Also! If you’re looking for more statistics, check out this post on how to create and analyze box and whisker plots here!

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