Interquartile, Semi-Interquartile and Mid-quartile Ranges
The median of the lower half of a set of data is the lower quartile ( ) or .
The median of the upper half of a set of data is the upper quartile ( ) or .
The upper and lower quartiles can be used to find another measure of variation call the interquartile range .
The interquartile range or is the range of the middle half of a set of data. It is the difference between the upper quartile and the lower quartile.
Interquartile range =
In the above example, the lower quartile is and the upper quartile is .
The interquartile range is or .
Data that is more than times the value of the interquartile range beyond the quartiles are called outliers .
Statisticians sometimes also use the terms semi-interquartile range and mid-quartile range .
The semi-interquartile range is one-half the difference between the first and third quartiles. It is half the distance needed to cover half the scores. The semi-interquartile range is affected very little by extreme scores. This makes it a good measure of spread for skewed distributions. It is obtained by evaluating .
The mid-quartile range is the numerical value midway between the first and third quartile. It is one-half the sum of the first and third quartiles. It is obtained by evaluating .
(The median, midrange and mid-quartile are not always the same value, although they may be.)