Measures of Variance
The Variance
Learning Objectives
Calculate and understand the sample and population variances.
The Variance (Var):
- The Variance is the square of the Standard Deviation.
- It is rarely used in an introductory course in Statistics.
The SAMPLE variance is defined as:
[latex]s^2= \frac{\Sigma(x_i-\bar{x})^2}{n-1}[/latex]
The POPULATION variance is defined as:
[latex]\sigma ^2= \frac{ \Sigma (x_i - \bar{x} ) ^2 }{ n-1}[/latex]
Example 7.1 – Variances of Sunita and Sanjay’s Grades (Excel)
Let us revisit Sunita and Sanjay’s grades. Let us now calculate the sample variance for each in Excel:
- Again, we see that Sanjay’s grades are much more ‘dispersed’ than Sunita’s
- The variance for Sanjay’s grades is much larger than Sunita’s variance for her grades.
- Click here to download the spreadsheet shown above.
Key Takeaways
Key Takeaways: The Variance
- The variance is the squared standard deviation.
- The variance is not often used in this course.
- There are different formulas for the sample and population variance.
- Often, we assume that we have a sample (if nothing is stated).
Your Own Notes
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- These notes are for you only (they will not be stored anywhere)
- Make sure to download them at the end to use as a reference
