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## Chapter 6

# Measures of Variation

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Version 2

By Boundless

By Boundless

Boundless Statistics

Statistics

by Boundless

Section 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.

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