# Variability

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With the addition of a constant value to each observation in a dataset, there is no change in the values. Hence all measures of variability are unchanged by the addition of constant value.

With the multiplication of a constant value to each observation in a data set the distance between values changes. Hence new range, interquartile range (IQR), and the standard deviation are constant multiplied by old range, interquartile range (IQR), and standard deviation respectively. And new variance is constant multiplied by old variance.

Variance

It is a measure of the spread of distribution about its mean. Variance measures the dispersion in squared units of the data. The less value of variance implies that the mean is reliable. For formula for population variance and sample variance differs in the denominator.

In statistical analysis data in form of sample and hence I use sample variance. Excel functions for population variance and sample variance is VAR.P and VAR.S respectively.

Some properties of variance for a random variable “X” with a constant “a” are:

For two random variables X and Y,

Standard Deviation

It is a measure of the spread of distribution about its mean. Standard Deviation measures the dispersion in original units of the data. The less value of Standard Deviation implies that the mean is reliable. For formula for population variance and sample Standard Deviation differs in the denominator.

In statistical analysis data in form of sample and hence I use sample Standard Deviation. Excel functions for population variance and sample variance is STDEV.P and STDEV.S respectively.

Range

The range is defined as the difference between the lowest and highest values in a dataset.

Interquartile Range

The interquartile range is defined as the difference of 3rd and 1st quartile. It is the best measure of dispersion in when data is skewed or has outliers.

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