, the interquartile range
refers to the overall difference between the higher quartile value of a data
set and the accompanying lower quartile value. A data set can be split up into three quartiles when you consider the whole set of values to be out of 100%. This is how the three quartiles can be defined:
Q1 = this is the first quartile and represents the first 25% of the data, also known as the 25th percentile
Q2 = this is the second quartile and represents the median
of the data, also known as the 50th percentile.
Q3 = this is the third quartile and represents the first 75% of the data, also known as the 75th percentile.
To find the interquartile range, the first quartile needs to be subtracted from the third quartile. Therefore, the formula is: Q3- Q1 = interquartile range.
For example, you are given a data set in which Q1 = 22.3, Q2 = 40.8 and Q3 = 65.3. What is the interquartile range?
= Q3 – Q1
= 65.3 – 22.3
Additionally, the interquartile range can be determined from a box plot
. In a box plot, quartiles are marked on the figure directly and so, when analyzing a box plot, the values for Q1 and Q3 can be identified, and thus, the interquartile range can be derived. By obtaining the interquartile range, the amount of variation which exists around the median can be interpreted. Therefore, just like other quantitative measures, the interquartile range represents another method of describing a data set.