- Describe the differences in variability in histograms and dotplots.
- Calculate and describe standard deviation.
Variance
Another measure of spread is called variance. Variance is the squared value of the standard deviation. Similar to standard deviation, the larger the value of the variance, the larger the variability of the data set. The smaller the value of the variance, the smaller variability exists within the data set.
variance
Variance is the standard deviation squared, [latex]\sigma^{2}[/latex] or [latex]s^{2}[/latex].
Variance of a population: [latex]\sigma^{2}=\dfrac{\sum\left(x-\mu\right)^{2}}{n}[/latex]
Variance of a sample: [latex]s^{2}=\dfrac{\sum\left(x-\bar{x}\right)^{2}}{n-1}[/latex]
The statistical tool does not calculate variance, so you will need to use the tool to calculate the standard deviation and then square it by hand or calculator in order to get the variance.