Measures of Variability

Understanding measures of variability

Descriptive statistics are used to summarize a data set. Measures of variability are used to quantify how spread out the values are around the center of the data. They provide a single value that can be helpful for quickly understanding the general characteristics of measured values. Some key measures of variability are:

• Standard deviation: the square root of the average squared distance to the mean.
• Variance: the average squared distance to the mean.
• Coefficient of variation: a unitless measure of variability.
• Quantiles, including percentiles and quartiles: specific locations in the data, comparisons among quantiles give measures of variability.
• Range: the distance from the minimum value to the maximum value of the data.
• Interquartile range: the range of the inner quartiles.

Different measures of variability are appropriate in different situations. The choice of which to use depends on the characteristics of your data and the specific goals of your analysis.

What are characteristics of various measures of variability?

Characteristics of the variance and standard deviation

• The variance is the average squared distance of the data values from the mean of the data values, measured in squared data units.
• The standard deviation is the square root of the variance, measured in the same units as the data.
• Their values are influenced by extreme values in the data.

Characteristics of the coefficient of variation

• The coefficient of variation is a unitless measure of variation.
• It is the standard deviation of the data, divided by the mean, multiplied by 100.
• It can be made smaller by reducing variability or by increasing the mean.

Characteristics of the quantiles, percentiles, and quartiles

• Quantiles separate the data into groups according to how much data is in each group.
• Percentiles break the data into hundredths.
• Quartiles break the data into fourths.
• Quantiles are not necessarily data values but can be between data values. Therefore, quantiles are not necessarily unique.
• The median is the 50^th percentile and the second quartile.
• Technically, quantiles are measures of location, but when you compare between them, like with the interquartile range, the comparison is a measure of variability.

Characteristics of the range

• It is the maximum value of the data minus the minimum value of the data.
• It is highly influenced by extreme values.
• It is typically used only when calculation of variability is difficult, specifically when variability is calculated by hand.

Characteristics of the interquartile range

• The interquartile range is the difference between the third and first quartile of the data values.
• It is not influenced by extreme values.