Measures of Dispersion

Measures of Dispersion

Numerical descriptions that provide information about the spread of data points in relation to the center of the data.

Range

The difference between the largest and smallest values in a dataset.

Variance

A measure of how far the data values are spread out from the mean, calculated as the average of the squared deviations from the mean.

Standard Deviation

A measure that indicates the amount of variation or dispersion of a set of values, providing an average distance from the mean.

Coefficient of Variation (CV)

The ratio of the standard deviation to the mean, expressed as a percentage, used to compare the relative variability of different datasets.

Empirical Rule

A statistical rule stating that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation, 95% within two, and 99.7% within three standard deviations of the mean.

Chebyshev's Theorem

A theorem stating that for any data distribution, at least 1 - (1/k^2) of the data values lie within k standard deviations of the mean, for k greater than 1.

Population Variance

The variance calculated for an entire population, denoted by sigma squared (σ²).

Sample Variance

The variance calculated from a sample of data, denoted by s squared (s²).

Population Standard Deviation

The standard deviation of an entire population, denoted by sigma (σ).

Sample Standard Deviation

The standard deviation calculated from a sample of data, denoted by s.

Biased Estimator

An estimator that tends to systematically overestimate or underestimate a parameter.

Class Midpoint

The value that is halfway between the upper and lower boundaries of a class in a frequency distribution.