1. Descriptive Statistics: Measures of Variability
Range, Interquartile Range, and the Five-Number Summary
The most basic measure of variability is the range.
Range
Definition
The range is the difference between the highest and the lowest score of a distribution.
Formula
Since the range measures variability by looking at the end-points of a distribution, it is extremely sensitive to the presence of outliers in the dataset. An alternative measure of variability that is much less sensitive to outliers is the interquartile range.
Interquartile range
Definition
The interquartile range (IQR) is the difference between the first quartile and the third quartile of a distribution.
Formula
Remember that quartiles are measures of location which divide a distribution into four equal parts, similar to how the median divides a distribution into two equal parts. The interquartile range thus measures how spread out the middle 50% of the data is. This means that the interquartile range is completely unaffected by the values of the smallest and largest 25% of the scores.
Often, the range and interquartile range are combined with the median to form a so-called five-number summary.
Five-number summary
Definition
The five-number summary is made up out of the following five points of a distribution:
- Minimum
- First quartile
- Median
- Third quartile
- Maximum
To plot the five-number summary, construct a boxplot.
Boxplot