Identify outliers in a data set

An outlier is a data value that lies unusually far from the overall pattern, identified from tables, dot plots, or box plots and, when quartiles are given, commonly by being below $Q_1-1.5\text{ IQR}$ or above $Q_3+1.5\text{ IQR}$ . The interpretation depends on context: an outlier may be a valid observation rather than an error and can substantially affect the mean and range while having less effect on the median; advanced statistical outlier tests and multivariable methods are not included.

Detailed Explanation: Identify outliers in a data set

An outlier is a data value that is unusually far from the other values. You can often spot one as a value separated from the main group in a table or dot plot.

When quartiles are available, use these steps:

Find the interquartile range:

\text{IQR}=Q_3-Q_1

Find the lower and upper fences:

\text{Lower fence}=Q_1-1.5(\text{IQR})

\text{Upper fence}=Q_3+1.5(\text{IQR})

Any value below the lower fence or above the upper fence is an outlier.

Example

The numbers of minutes 8 students spent commuting to school are:

8,\ 9,\ 10,\ 11,\ 12,\ 13,\ 14,\ 30

The data is already in order.

Step 1: Find $Q_1$ and $Q_3$ .

The lower half is $8,9,10,11$ , so

Q_1=\frac{9+10}{2}=9.5

The upper half is $12,13,14,30$ , so

Q_3=\frac{13+14}{2}=13.5

Step 2: Find the IQR.

\text{IQR}=13.5-9.5=4

Step 3: Find the fences.

\text{Lower fence}=9.5-1.5(4)=3.5

\text{Upper fence}=13.5+1.5(4)=19.5

Step 4: Compare the data values with the fences.

No value is below $3.5$ . However, $30$ is above $19.5$ .

Therefore, $30$ minutes is an outlier.

The value $30$ is not automatically an error. It could represent a student who lives much farther away. An outlier can affect the mean and range greatly, while usually having less effect on the median.

Learn by doing: Identify outliers in a data set

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Statistics - Quartiles - Median, Q1, Q3 and Point to Is Outlier

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