Measures of Variability and Boxplots in Statistics

Range

The difference between the largest and smallest sample values.

Deviation from the Mean

The difference between each sample observation and the mean, where positive deviations are larger than the mean and negative deviations are smaller.

Average Absolute Deviation

The average of the absolute values of the deviations from the mean.

Average Squared Deviation

The sum of squared deviations divided by n - 1.

s^2

The sample variance, always nonnegative and with the same unit as the sample observations.

Boxplot

A graphical representation of the five-number summary: smallest value, lower quartile, median, upper quartile, and largest value.

Interquartile Range (IQR)

The difference between the upper and lower quartiles, Q3 - Q1.

Standard Error of the Mean (SE Mean)

The standard error associated with the sample mean, crucial for making inferences about the population mean.