# Measures of Variation

## 6.1 Describing Variability

#### Range

The range is a measure of the total spread of values in a quantitative dataset.

#### Variance

Variance is the sum of the probabilities that various outcomes will occur multiplied by the squared deviations from the average of the random variable.

#### Standard Deviation: Definition and Calculation

Standard deviation is a measure of the average distance between the values of the data in the set and the mean.

#### Interpreting the Standard Deviation

The practical value of understanding the standard deviation of a set of values is in appreciating how much variation there is from the mean.

#### Using a Statistical Calculator

For advanced calculating and graphing, it is often very helpful for students and statisticians to have access to statistical calculators.

#### Degrees of Freedom

The number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

#### Interquartile Range

The interquartile range (IQR) is a measure of statistical dispersion, or variability, based on dividing a data set into quartiles.

#### Measures of Variability of Qualitative and Ranked Data

Variability for qualitative data is measured in terms of how often observations differ from one another.

#### Distorting the Truth with Descriptive Statistics

Descriptive statistics can be manipulated in many ways that can be misleading, including the changing of scale and statistical bias.

#### Exploratory Data Analysis (EDA)

Exploratory data analysis is an approach to analyzing data sets in order to summarize their main characteristics, often with visual methods.