interquartile range
The difference between the first and third quartiles; a robust measure of sample dispersion.
Examples of interquartile range in the following topics:

Interquartile Range
 The interquartile range (IQR) is a measure of statistical dispersion, or variability, based on dividing a data set into quartiles.
 The interquartile range (IQR) is a measure of statistical dispersion, or variability, based on dividing a data set into quartiles.
 The interquartile range is equal to the difference between the upper and lower quartiles:
 Unlike (total) range, the interquartile range has a breakdown point of 25%.
 In other words, since this process excludes outliers, the interquartile range is a more accurate representation of the "spread" of the data than range.

Measures of Variability
 There are four frequently used measures of variability: range, interquartile range, variance, and standard deviation.
 The interquartile range (IQR) is the range of the middle 50% of the scores in a distribution.
 For Quiz 2, which has greater spread, the 75th percentile is 9, the 25th percentile is 5, and the interquartile range is 4.
 Using this terminology, the interquartile range is referred to as the Hspread.
 The semiinterquartile range is defined simply as the interquartile range divided by 2.

Exercises
 For the test scores in question #6, which measures of variability (range, standard deviation, variance) would be changed if the 22.1 data point had been erroneously recorded as 21.2?
 : mean, median, mode, trimean, geometric mean, range, interquartile range, variance, standard deviation
 (SL#2) Find the mean, median, standard deviation, and interquartile range for the leniency scores of each of the four groups.
 (AT#7) What are the standard deviation and the interquartile range of the d0 condition?

Box plots, quartiles, and the median
 The total length of the box, shown vertically in Figure 1.25, is called the interquartile range (IQR, for short).

The Density Scale
 In addition to the points themselves, box plots allow one to visually estimate the interquartile range.
 A range of data clustering techniques are used as approaches to density estimation, with the most basic form being a rescaled histogram.
 For the histogram, first the horizontal axis is divided into subintervals, or bins, which cover the range of the data.

Outliers
 Another method often used is based on the interquartile range (IQR).

Measures of the Location of the Data
 The interquartile range is a number that indicates the spread of the middle half or the middle 50% of the data.

Outliers
 Other methods flag observations based on measures such as the interquartile range (IQR).
 Rhode Island, Texas, and Alaska are outside the normal data range, and therefore are considered outliers in this case.

Graphs of Qualitative Data
 Median, measures of shape, measures of spread such as the range and interquartile range, require an ordered data set with a logical lowend value and highend value.

Box Plots
 Interquartile Range: IQR = Q3 − Q1 = 70 − 64.5 = 5.5.
 The middle 50% (middle half) of the data has a range of 5.5 inches.