Example, with R
The most common range (or 'interval') is given by the maximum and minimum.
As in: "exam results ranged from good to excellent last year"
The range is most often applied to numeric data, such as the percentage of each class achieving at least a C-grade pass.
Given the data, you can readily find their range with R
Definition and Use
- A range is two numbers, most commonly the maximum or minimum, used to indicate variation within a set of numbers.
- An interval is one number, most commonly the difference between the maximum or minimum.
- More generally: a range or interval may be used to describe any two numbers or the difference between them.
For instance:
- the interquartile range is either the first and third quartiles, or the difference between them.
- the 90% range is either the 5% or 95% quantiles, or the difference between those two values.
- Class-intervals refer to arbitrarily set 'breakpoints' used to divide a set of numbers into equal width ranges in order to plot a histogram or bargraph.
- Confidence intervals are another sort of range, but are applied to the observed value of summary statistics - however these are not simple measures of data variation.
Simple formula
Provided y contains a list of numbers, the overall range of y is:
y_{minimum} and y_{maximum}
or
y_{maximum} minus y_{minimum}
Tips and Notes
- Ranges can be useful to summarize how numbers are distributed.
- The maximum and minimum are sometimes called the 100% range because they apply to all the available data.
- Since the minimum and maximum are the most extreme values (of lowest and highest rank) they are often the least representative values - and, in some circumstances, may be correspondingly less useful measures of variation.
- The interquartile range defines the most typical half of values, and is correspondingly more representative.
- The 95% range encloses 95% of values - all but the lowest and highest 2.5% of values - assuming there are sufficiently many values...
- Subject to various assumptions, ranges can (arbitrarily) define what is typical from what is exceptional.
Test yourself
Useful references
- Wikipedia: Range (statistics).
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