Five-Number Summary & Boxplots (College Board AP® Statistics)
Study Guide
Written by: Mark Curtis
Reviewed by: Dan Finlay
Five-number summary
What is a five-number summary?
A five-number summary is the collection of the following five values from a data set:
the minimum data value
the first quartile (Q1)
the median (Q2)
the third quartile (Q3)
the maximum data value
It is a concise way to summarise a set of data without showing all the data values
What can I calculate from a five-number summary?
From a five-number summary, you can:
find a measure of the center of the data
The median
find a measure of the spread (variability) of the data
Either the range (maximum - minimum)
or the interquartile range (Q3 - Q1)
find the shape of the distribution of the data
by comparing the difference Q2 - Q1 with the difference Q3 - Q2
Boxplots
What is a boxplot?
A boxplot is a graph that shows the five-number summary
The minimum data value, first quartile, median, third quartile and maximum data value of a set of data
A box is used to represent the middle 50% of the data
The width of the box is the interquartile range
The difference between the first and third quartile (also known as the lower and upper quartiles)
Two whiskers (horizontal lines) are extended from either side of the box to the minimum data value and the maximum data value
The median is shown by a vertical line inside the box
This is not necessarily in the center of the box
Outliers (extreme values) are represented with a cross and are outside of the whiskers
The maximum and minimum data values do not include outliers
The whisker ends at the value before the outlier
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