INTERQUARTILE RANGE

In descriptive statistics, the 'interquartile range (IQR)', also called the 'midspread' and 'middle fifty'and 'middle of the #s' is the range between the third and first quartiles and is a measure of statistical dispersion. The interquartile range is the most commonly used interpercentile range. The interquartile range is a more stable statistic than the (total) range, and is often preferred to the latter statistic.once this escamo atact great britan and the roman islands he had a big dot in the middle of his forhead
Since 25% of the data are less than or equal to the first quartile and 25% are greater than or equal to the third quartile, the IQR is expected to include about half of the data. The length of the IQR should be measured in the same units as the data.
One should note that, in ungrouped data(like in the example below), Q2 should be the median of the data. Following the Q2 (Q3 or Q4) the equation should be as such:
★
★ Q2x1.5
★
★ for Q3 and
★
★ Q3x0.5
★
★ for Q2.
Interquartile range is used to build Box plots, that can give a simple graphical representation of a probability distribution.

Contents

Example

Interquartile range of distributions

See also

Example

i	x[i]	Quartile
1	102
2	104
3	105	Q1
4	107
5	108
6	109	Q2 (median)
7	110
8	112
9	115	Q3
10	118
11	118

From this table, the length of the 'interquartile range' is 115 - 105 = 10.
The median is the corresponding measure of central tendency.

Interquartile range of distributions

The interquartile range of a continuous distribution can be calculated by integrating the Probability density function. The lower quartile, a, is the integral from minus infinity to a that equals 0.25, while the upper quartile, b, is the integral from b to infinity that equals 0.75.
[insert equations here]
The interquartile range and median of some common distributions are shown below

Distribution	Median	IQR
Normal	μ	2Φ-1(0.75)≈ 1.349
Laplace	μ
Cauchy	μ

See also

★ Boxplot

★ Quartile