Why calculators give different quartiles
There is no single definition of a quartile. When the 25% point falls between two data values, each method handles it differently, so Excel, a TI-84 and your textbook can all disagree on the same data. This calculator shows the three most common methods together, which makes it easy to match the answer your course expects. The reasons are explained in how to find quartiles and the IQR.
Worked example
For 3, 5, 7, 8, 12, 13, 14, 18, 21 (n = 9), the median is 12. The inclusive method gives Q1 = 7 and Q3 = 14 (IQR = 7). The exclusive method and the median-of-halves method both give Q1 = 6 and Q3 = 16 (IQR = 10). The difference is large here because the sample is small, and it shrinks as the sample grows.
Which method should I use?
- For coursework: use the method in your textbook or the calculator your course requires.
- In Excel or R: the default is the inclusive method.
- In a report: name the software or method, especially with small samples.
Accuracy
The inclusive and exclusive results match NumPy’s linear and weibull methods (equivalent to R types 7 and 6) on samples of 4 to 31 values. To flag unusual values with the IQR, use the outlier calculator.
Frequently asked questions
Why does my calculator give a different Q1 than Excel?
Excel's QUARTILE.INC and most hand methods use different rules when a quartile falls between data values. Both answers are valid under their own definition.
How do you calculate the IQR?
Subtract the first quartile from the third: IQR = Q3 - Q1. It covers the middle 50% of the data.
Is the median included when finding quartiles?
It depends on the method. The median-of-halves method used here and on TI-84 calculators leaves it out when n is odd. Tukey's hinges include it.
Which quartile method does R use?
R's quantile function uses type 7 by default, which is the inclusive method shown here.