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Mathematics · pattern F, Dataset

Range, quartiles and interquartile range.

Paste your data for the range, the quartiles and the IQR — the spread measure that ignores outliers instead of being dominated by them.

Inputs

Sample or population

Divide by n − 1 for a sample drawn from a wider population; by n only when the data is the entire population.

The formula used

range = maximum − minimum; IQR = Q3 − Q1

The range uses only two values, so one extreme point sets it entirely. The interquartile range covers the middle half and is far more robust.

Range

76.000

n = 10 · sample, ÷ (n − 1)

n
10
Sum
281.000
Mean
28.100
Median
23.000
Mode
no repeated value
Σ(x − x̄)²
4,276.900
Variance
475.211
Standard deviation
21.799
Standard error
6.8936
Minimum / maximum
12.00 / 88.00
Range
76.000
Q1 / Q3 / IQR
18.25 / 26.50 / 8.25

Your data — accent bars sit beyond one deviation

12.0088.00

One outlier destroys the range.

In the default data the range is 76 while the interquartile range is about nine, because a single value of 88 sets the range by itself. This is why box plots are built on quartiles, and why anything beyond 1.5 IQR from a quartile is conventionally flagged as an outlier.

Questions about range

What is the interquartile range?
The distance between the first and third quartiles, covering the middle 50% of the data and unaffected by extremes.
How are outliers defined?
Conventionally more than 1.5 IQR beyond a quartile. It is a convention rather than a test, and context should override it.
Why do quartiles differ between software?
Several interpolation methods exist and they disagree on small samples. State the method where it matters.

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