Min, Q1, median, Q3, max
Five Number Summary Calculator with Quartiles and IQR
Get the minimum, Q1, median, Q3 and maximum of a data set, plus the IQR, range and outliers by the 1.5 × IQR rule, with the halves used for each quartile shown.
Sorted (11): 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49. Fences: -27 and 85.
Lower half: 6, 7, 15, 36, 39. Upper half: 41, 42, 43, 47, 49. The median is left out of both halves because the count is odd.
Every value is calculated in your browser from the standard normal distribution (Marsaglia’s series for Φ) and rounded to four decimals; the tables were checked cell by cell against an independent calculation. These tables give the area to the left of z. Some textbooks, including the NIST handbook, print the area from 0 to z instead, which is the left area minus 0.5 for positive z.
How the quartiles are found
Sort the data and find the median. With the median-of-halves method, Q1 is the median of the lower half and Q3 the median of the upper half, leaving the overall median out of both halves when the count is odd. For 6, 7, 15, 36, 39, 40, 41, 42, 43, 47 and 49 this gives Q1 = 15, median = 40 and Q3 = 43. Linear interpolation (Excel’s QUARTILE.INC) gives Q1 = 25.5 and Q3 = 42.5 for the same data.
- IQR = Q3 − Q1.
- Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are flagged as outliers.
Common questions
Why does my calculator give a different Q1?
Quartile methods differ. TI-84 calculators and most U.S. statistics classes use the median of each half; Excel’s QUARTILE.INC interpolates. Switch the method to match yours.
What is the IQR used for?
The interquartile range measures the spread of the middle half of the data, and it sets the fences used to flag outliers.
The studio notebook
A useful place to begin.
Clear steps, considered details, and ideas you can put to use.
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