Measures of Dispersion

Measures of dispersion provide information about the spread of data or how much the data varies. The most common measures of dispersion are range, variance, standard deviation, and interquartile range.

Range

The range is the difference between the highest and lowest values in a dataset. It provides a rough idea of how spread out the values are.

Range = Maximum value - Minimum value

Variance

Variance measures how far each number in the set is from the mean and thus from every other number in the set. It’s often denoted by the symbols σ² for the population variance and s² for the sample variance.

Variance = Sum of (each data point - mean)² / Number of data points

Standard Deviation

The standard deviation is the square root of the variance. It is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

Standard Deviation = √Variance

Interquartile Range (IQR)

The interquartile range is a measure of variability that eliminates the influence of outliers or extreme values. It is calculated as the difference between the first quartile (25th percentile) and the third quartile (75th percentile).

IQR = Q3 - Q1

These measures of dispersion are useful in statistics because they provide a way to understand the spread and variability in your data.