Using a fence to find outliers

We have recently explored calculating the five number summary and drawing a box and whisker plot.

Once we have our minimum, lower quartile, median, upper quartile and maximum, we can use this information to determine whether a data point can be considered an outlier.

To do this, we calculate what we like to call the fences.

Once we have calculated the lower fence and the upper fence, any data that falls within the fence lines is not an outlier.

Any data that fall outside the fence lines will be considered an outlier.

Worked Example:

Consider the box plot given below.

By calculating the lower and upper fence, detemine whether the data points $4$4 and $32$32 can be considered outliers. 

Think: Firstly we need to calculate the lower and upper fence.

Do: 

Lower fence = $11-1.5\times8$11−1.5×8

Lower fence = $-1$−1

Upper fence = $19+1.5\times8$19+1.5×8

Upper fence = $31$31

Think: Does $4$4 lie inside or outside the fence?

Do: Since $4$4 is above the lower fence of $-1$−1, it is inside the fence and hence not an outlier.

Think: Does $32$32 lie inside or outside the fence?

Do: Since $32$32 is above the upper fence of $31$31, it is outside the fence and hence an outlier.

 

Worked Examples

Question 1

Question 2

Question 3