# Quartiles

Quartile is a percentile measure that divides the total of 100% into four equal parts: 25%, 50%, 75% and 100%.  A particular quartile is the border between two neighboring quarters of the distribution.

Q1 (quartile 1) separates the bottom 25% of the ranked data (Data is ranked when it is arranged in order.) from the top 75%.  Q2 (quartile 2) is the mean or average.  Q3 (quartile 3) separates the top 25% of the ranked data from the bottom 75%.  More precisely, at least 25 % of the data will be less than or equal to Q1 and at least 75% will be greater than or equal Q1.  At least 75% of the data will be less than or equal to Q3 while at least 25% of the data will be greater than or equal to Q3.

Interquartile range is the distance between the first and third quartiles. It is sometimes called the H-spread and is a stable measure of disbursement.  It is obtained by evaluating Q3Q1.

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 midquartile 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 midquartile are not always the same value, although they may be.)