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 Q3– Q1.
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.)