Key Concepts

• Standard deviation describes the typical distance a value is from the mean.
• Variance is the square of the standard deviation.
• There is a slight difference in the formula for calculating standard deviation of a population versus the standard deviation of a sample. When calculating standard deviation of a population, you divide by n. When calculating the standard deviation of a sample, you divide by n – 1.

Glossary

radical symbol: the symbol for the square root. It looks like this: [latex]\sqrt{\,\,\,}[/latex]

radicand: the number that is written under the radical symbol

sampling variability: how much the statistic varies from one sample

standard deviation: a number that is equal to the square root of the variance and measures how far data values are from their mean. Notation: s for sample standard deviation and σ for population standard deviation.

variance: mean of the squared deviations from the mean, or the square of the standard deviation. The sample variance is equal to the sum of the squares of the deviations divided by the difference of the sample size and one.

z-score: to determine the number of standard deviations a value is above or below the mean, a z-score is calculated. Values above the mean have a positive z-score and values below the mean have a negative z-score. The formula for a z-score is [latex]z=\frac{\mathrm{value} - \mathrm{mean}}{\mathrm{standard \ deviation}}[/latex].