Measures of Variation

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Variation is the enemy of most processes. Popular measures include the range, variance, and standard deviation.

Range


Purpose

The range is used to measure data dispersion between the highest and the lowest values of a sample. This is one of the measurements that evaluates the variation between values.


Anatomy

Measures of Variation, Range

Terminology

A. R: Represents the range. It is an estimator of the population standard deviation.

B. The largest value in the data set.

C. The smallest value in the data set.


Major Considerations

Since the RANGE only considers extreme values, it may be an imprecise dispersion measure.

Application Cookbook

1. Use Minitab to calculate the Range:

Use the following function in Calc>Column Statistics and choose Range as statistic.

Variance


Purpose

Variance is used to determine the variability in a set of data. It is important to measure the extent to which data are scattered around the zone of central tendency, the mean, because this variation causes defects.

Variance is the sum of squares of the difference between each observation and the average divided by the degrees of freedom.

Anatomy

Formula For Variance

Terminology

A. Upper case S-squared is used to signify "population variance". Lower case s-squared is used to represent the sample variance.

B. xi represents the ith value of X.

C. x bar is used to denote the sample mean. mu represents the population mean.

D. Degrees of Freedom (n-1), where the lower case "n" is sample size.

The population variance does not use n-1 in the denominator. Population size is designated with an upper case N.


Major Considerations

The variance is a good measure of dispersion, but it suffers from one disadvantage: it is difficult to interpret the numerical value of the variance because the units of measure are squared. It is often more convenient to calculate the square root of the variance, which is referred to as the standard deviation.

Application Cookbook

To calculate the VARIANCE: Use Excel to calculate the variance of a data set, use the statistical function VAR.

From Variation to Six Sigma Tools.

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