In statistics, we tend to assume that our data will fit some kind of trend and that most things will fit into a "normal" range, even though we expect a certain amount of variability. This is why we look at measures of central tendency, such as the mean, median and mode, and talk about the normal distribution, which is a nice symmetrical graph shaped like a bell.

An outlier is an event that is very different from the norm and results in a score that is really above or below average. For example, if there are 10 people in a long jump contest and nine people can jump between 4 and 5 metres, and one person only jumped 1 metre, they would be an outlier as their jump is much shorter than everyone else in the group.

Outliers can affect our measures of central tendency and variability, which we will learn about later in Things Out of the Norm. However, let's look at some examples of how to identify outliers now.

Worked Examples

Question 1

Identify the outlier(s) in the data set $\left\{73,77,81,86,131\right\}${73,77,81,86,131}.

QUESTION 2

The graph shows the annual net profit (in millions) of a company over a several year period. Identify the year in which the annual net profit is an outlier.

QUESTION 3

VO₂ Max is a measure of how efficiently your body uses oxygen during exercise. The more physically fit you are, the higher your VO₂ Max. Here are some people’s results when their VO₂ Max was measured.

$46,27,32,46,30,25,41,24,26,29,21,21,26,47,21,30,41,26,28,26,76$46,27,32,46,30,25,41,24,26,29,21,21,26,47,21,30,41,26,28,26,76

Sort the values into ascending order.
Determine the median VO₂ Max.
Determine the upper quartile value. Leave your answer as a decimal if necessary.
Determine the lower quartile value. Leave your answer as a decimal if necessary.
Calculate $1.5\times IQR$1.5×IQR, where IQR is the interquartile range. Leave your answer as a decimal if necessary.
An outlier is a score that is more than $1.5\times IQR$1.5×IQR above or below the Upper Quartile or Lower Quartile respectively. State the outlier.
Here is a box and whisker plot for the data.

An average untrained healthy person has a VO₂ Max between $30$30 and $40$40. The majority of this group of people are likely to:
do moderate amounts of exercise
A
be professional athletes
B
do none to moderate amounts of exercise
C

Outcomes

12D.D.1.5

Interpret statistical summaries to describe the characteristics of a one-variable data set and to compare two related one-variable data sets; describe how statistical summaries can be used to misrepresent one-variable data; and make inferences, and make and justify conclusions, from statistical summaries of one-variable data orally and in writing, using convincing arguments

Identify outliers