Measures of Dispersion for Ungrouped Data

Interquartile range

The spread of the middle half of the data, from the first to the third quartile.

EnglishInterquartile range
Bahasa MelayuJulat antara kuartil
中文四分位距

How it is used

For 3, 5, 7, 9, 11, 13, 15 the median is 9. The lower half 3, 5, 7 gives Q1 = 5 and the upper half 11, 13, 15 gives Q3 = 13, so the interquartile range is 13 − 5 = 8.

Where it shows up in SPM

In Measures of Dispersion for ungrouped data. Paper 1 may ask for Q1, Q3 or their difference from an ordered list; Paper 2 links it to a box plot or asks you to compare the spread of two groups using the middle half.

Don't confuse it with

RangeThe interquartile range spans only from Q1 to Q3, so unlike the ordinary range it is not distorted by extreme values.
MedianThe median is the second quartile Q2, a single central value, while the interquartile range is the distance Q3 − Q1 around it.

Open the chapter: Measures of Dispersion for Ungrouped Data →

Frequently asked questions

How do I find the quartiles when there is an odd number of values?

Order the data, take the median as the middle value, then exclude it. The lower half gives Q1 as its median and the upper half gives Q3.

For 3, 5, 7, 9, 11, 13, 15 you drop the 9, so Q1 = 5 and Q3 = 13.

When is the interquartile range better than the range?

When the data contains outliers. Because it looks only at the middle 50 percent, a single very large or very small value does not change it, so it gives a fairer picture of the typical spread than the range does.

Related terms

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