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Use/Abuse Stat.Book Beginners Stats & R
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Beginners statistics:


On this page: Example, with R,  Definition and Use,  Simple formula,  Tips and Notes,  Test yourself,  References  Download R  R is Free, very powerful, and does the boring calculations & graphs for scientists.

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 

Definition and Use

  1. A range is two numbers, most commonly the maximum or minimum, used to indicate variation within a set of numbers.
  2. An interval is one number, most commonly the difference between the maximum or minimum.
  3. 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:

yminimum and ymaximum


ymaximum minus yminimum

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). Full text