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Range is a measure of spread that measures the difference between the maximum and minimum values of the data set.
The interquartile range, or IQR, of a data set is a measure of spread that measures the difference between Q3 and Q1, the upper and lower quartiles.
IQR=Q3−Q1
The following applet shows how to find the IQR of different data sets.
The mean absolute deviation (MAD) is a measure of the spread of a data set that measures how much the data elements differ from the mean. The mean absolute deviation is the average distance between each data value and the mean.
For each data value, x−x can now be calculated and added to a table. This shows how much each data point varies from the mean.
x | x−x |
---|---|
1 | 1−5=-4 |
5 | 5−5=0 |
3 | 3−5=-2 |
4 | 4−5=-1 |
5 | 5−5=0 |
12 | 12−5=7 |
Square the deviations, and add them to a new column in the table.
x | x−xˉ | (x−xˉ)2 |
---|---|---|
1 | -4 | (-4)2=16 |
5 | 0 | 02=0 |
3 | -2 | (-2)2=4 |
4 | -1 | (-1)2=1 |
5 | 0 | 02=0 |
12 | 7 | 72=49 |