Learn About Measures of Variation

Measures of Variation

Measures of variation are used to describe the distribution or spread of data. 

Range

The range is the difference between the greatest and least data values. 

Quartiles

Quartiles are values that divide the data set into four equal parts.

The median divides the data in half.

Then, the lower quartile is the section of data from the lowest value to the median of the lower half.

The upper quartile is the section of data from the highest value to the median of the higher half.

Half of the data will reside in the interquartile range.

Mean Absolute Deviation (MAD)

The mean absolute deviation is the average distance between each data value and the mean.  This value tells how spread out the data is relative to the mean.

Example

Consider the data shown below.  Identify the range.  Display and describe the quartiles and find the mean absolute deviation.

7, 10, 15, 16, 18

Range

The range of the data is 18 - 7 = 11.

Quartiles

The median is 15.

The lower quartile is 10.

The upper quartile is 16.

The interquartile range is between 10 and 16, which can also be represented by the number 6 (16 - 10 = 6).

Mean Absolute Deviation

The mean is 13.2.

Each data point has the following distances from the mean:

13.2 - 7 = 6.2

13.2 - 10 = 3.2

15 - 13.2 = 1.8

16 - 13.2 = 2.8

18 - 13.2 = 4.8

The average of these distances is:  3.76

Mean Absolute Deviation = 3.76

Practice

Consider the data shown below.  Identify the range.  Display and describe the quartiles and find the mean absolute deviation.

Answers

Range:  5

Lower Quartile:  1

Median:  2

Upper Quartile:  3.5

Mean Absolute Deviation:  about 1.42