If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Statistics and probability

Course: Statistics and probability > Unit 3

Lesson 7: Box and whisker plots
Math
Statistics and probability
Summarizing quantitative data
Box and whisker plots
© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

Identifying outliers with the 1.5xIQR rule

Google Classroom
An outlier is a data point that lies outside the overall pattern in a distribution.
The distribution below shows the scores on a driver's test for 19 applicants. How many outliers do you see?
A dot plot has a horizontal axis labeled scores numbered from 0 to 25. Dots are plotted above the following: 5, 1; 7, 1; 10, 1; 15, 1; 19, 1; 21, 2; 22, 2; 23, 5; 24, 4; 25, 1.
Some people may say there are 5 outliers, but someone else might disagree and say there are 3 or 4 outliers. Statisticians have developed many ways to identify what should and shouldn't be called an outlier.
A commonly used rule says that a data point is an outlier if it is more than 1, point, 5, dot, start text, I, Q, R, end text above the third quartile or below the first quartile. Said differently, low outliers are below start text, Q, end text, start subscript, 1, end subscript, minus, 1, point, 5, dot, start text, I, Q, R, end text and high outliers are above start text, Q, end text, start subscript, 3, end subscript, plus, 1, point, 5, dot, start text, I, Q, R, end text.
Let's try it out on the distribution from above.

Step 1) Find the median, quartiles, and interquartile range

Here are the 19 scores listed out.
5, 7, 10, 15, 19, 21, 21, 22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 24, 25
What is the median?
start text, m, e, d, i, a, n, end text, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

What is the first quartile?
start text, Q, end text, start subscript, 1, end subscript, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

What is the third quartile?
start text, Q, end text, start subscript, 3, end subscript, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

What is the interquartile range?
start text, I, Q, R, end text, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Step 2) Calculate 1, point, 5, dot, start text, I, Q, R, end text below the first quartile and check for low outliers.

problem a
Calculate start text, Q, end text, start subscript, 1, end subscript, minus, 1, point, 5, dot, start text, I, Q, R, end text
start text, Q, end text, start subscript, 1, end subscript, minus, 1, point, 5, dot, start text, I, Q, R, end text, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

problem b
How many data points can we say are low outliers?
A dot plot has a horizontal axis labeled scores numbered from 0 to 25. Dots are plotted above the following: 5, 1; 7, 1; 10, 1; 15, 1; 19, 1; 21, 2; 22, 2; 23, 5; 24, 4; 25, 1.
Choose 1 answer:

Step 3) Calculate 1, point, 5, dot, start text, I, Q, R, end text above the third quartile and check for high outliers.

problem a
Calculate start text, Q, end text, start subscript, 3, end subscript, plus, 1, point, 5, dot, start text, I, Q, R, end text
start text, Q, end text, start subscript, 3, end subscript, plus, 1, point, 5, dot, start text, I, Q, R, end text, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

problem b
How many data points can we say are high outliers?
A dot plot has a horizontal axis labeled scores numbered from 0 to 25. Dots are plotted above the following: 5, 1; 7, 1; 10, 1; 15, 1; 19, 1; 21, 2; 22, 2; 23, 5; 24, 4; 25, 1.
Choose 1 answer:

Bonus learning: Showing outliers in box and whisker plots

Box and whisker plots will often show outliers as dots that are separate from the rest of the plot.
Here's a box and whisker plot of the distribution from above that does not show outliers.
A box and whisker plot above a line labeled scores. The left side of the whisker at 5. The beginning part of the box is at 19. The ending part of the box is at 24. The right side of the whisker is at 25.
Here's a box and whisker plot of the same distribution that does show outliers.
Notice how the outliers are shown as dots, and the whisker had to change. The whisker extends to the farthest point in the data set that wasn't an outlier, which was 15.
Here's the original data set again for comparison.
A dot plot has a horizontal axis labeled scores numbered from 0 to 25. Dots are plotted above the following: 5, 1; 7, 1; 10, 1; 15, 1; 19, 1; 21, 2; 22, 2; 23, 5; 24, 4; 25, 1.

Want to join the conversation?

Log in