What the five number summary shows
The five number summary captures a data set with five values: the minimum, first quartile (Q1), median, third quartile (Q3) and maximum. For 1, 2, 3, 4, 5, 6, 7, 8 the summary is 1, 2.5, 4.5, 6.5, 8. These five values are also the basis for a box-and-whisker plot. The middle of the five values is the median, and everything else is arranged around it.
How to use this calculator
Enter your numbers and leave unused fields blank. The big number is the median, and the badge lists the minimum, Q1, Q3 and maximum. For just the quartiles, use the quartile calculator.
The values do not need to be sorted — the tool orders them for you before splitting the set. At least two numbers are required, since quartiles need a lower and an upper half to work with.
Reading spread from the summary
The distance from minimum to maximum is the range, while Q3 − Q1 is the interquartile range describing the middle 50%. A median far from the centre of Q1 and Q3 hints at skew. To check for unusually high or low points, use the outlier calculator.
Frequently asked questions
- What is a five number summary?
- It is the minimum, first quartile (Q1), median, third quartile (Q3) and maximum of a data set. For 1–8 it is 1, 2.5, 4.5, 6.5, 8.
- How are the quartiles found?
- Sort the data, take the median, then find the median of the lower half (Q1) and upper half (Q3), excluding the middle value when the count is odd.
- Why is the five number summary useful?
- It summarizes the centre and spread of data in five numbers and is the basis for drawing a box-and-whisker plot.
- What is the range from this summary?
- The range is the maximum minus the minimum, here 8 − 1 = 7.
- Why does my textbook or spreadsheet give different quartiles?
- Because several quartile conventions exist. This tool uses the exclusive method that drops the median before splitting an odd-sized set, while Excel's QUARTILE.INC interpolates instead. Minimum, median and maximum always agree; only Q1 and Q3 can differ slightly.