Quartiles are values that divide a sample of data into four equal parts. With them you can quickly evaluate a data set's spread and central tendency, which are important first steps in understanding your data.

Quartile Description
1st quartile (Q1) 25% of the data are less than or equal to this value.
2nd quartile (Q2) The median. 50% of the data are less than or equal to this value.
3rd quartile (Q3) 75% of the data are less than or equal to this value.
Interquartile range The distance between the 1st and 3rd quartiles (Q3-Q1); thus, it spans the middle 50% of the data.
For example, for the following data: 7, 9, 16, 36, 39, 45, 45, 46, 48, 51
  • Q1 = 14.25
  • Q2 (median) = 42
  • Q3 = 46.50
  • Interquartile range = 14.25 to 46.50, or 32.25
Note

Quartiles are calculated values, not observations in the data. It is often necessary to interpolate between two observations to calculate a quartile accurately.

Because they are not affected by extreme observations, the median and interquartile range are a better measure of central tendency and spread for highly skewed data than are the mean and standard deviation.

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