Measures of spread: Range
In a nutshell
Measures of spread, also called measures of dispersion or variation, describe how spread out the data is.
Range
The range is the difference between the maximum and the minimum values of the data set.
Interquartile range
The interquartile range is the difference between the upper and the lower quartile.
IQR=Q3−Q1 | IQR | Interquartile range | Q3 | Upper quartile | Q1 | Lower quartile | |
Interpercentile range
The interpercentile range is the difference between the values of two chosen percentiles.
Note: The range is affected by extreme values, whereas the interquartile and interpercentile ranges aren't. However, the range takes into account all of the data, while the interquartile range only considers the middle 50%.
Example 1
For the following values, find the range, the interquartile range and the 10th to 90th interpercentile range.
3,5,5,7,9,10,12,12,15,16,20,20,21
The range will be given by:
Maximum−minimum=21−3=18
For the interquartile range you have to find each quartile:
Q1=413=3.25=4th value (rounding up).
Q3=413×3=9.75=10th value.
So, the lower quartile will be 7 and the upper quartile is 16.
Q3−Q1=16−7=9
Now, find the 10th and the 90th percentiles:
0.1×13=1.3≈2nd value (rounding up), which means P10=5.
0.9×13=11.7≈12th value, which means P90=20.
P90−P10=20−5=15