Interquartile Range (IQR)

The interquartile range (IQR) is a measure of statistical dispersion, representing the range between the first quartile (Q1) and the third quartile (Q3) in a data set.

IQR = Q3 - Q1, where Q3 is the third quartile and Q1 is the first quartile.

Q1 is the median of the lower half of a data set, meaning 25% of the data points are below this value.

Q3 is the median of the upper half of a data set, meaning 75% of the data points are below this value.

IQR = 10.5 - 3.5 = 7.

The IQR is used to measure the spread of the middle 50% of data points and to identify outliers.

The five-number summary includes the minimum, Q1, median, Q3, and maximum. The IQR is calculated as Q3 - Q1.

An outlier is a data point that is significantly different from other observations, often identified using the IQR.

Outliers can be identified as any data point that is below Q1 - 1.5*IQR or above Q3 + 1.5*IQR.

The difference in IQR between two data sets shows how the spread of the middle 50% of values compares between the two sets.