Find the difference between the measures of central tendency when the outlier is included and when it is not included.
The mean, see solution.
Practice makes perfect
We are asked to explain which measure of central tendency is most affected by an outlier. Let's take a look at the measures of central tendency from the previous two exercises.
Data set
Mean
Median
Mode
Exercise 1
With Outlier
22.8
19.5
18
Without Outlier
19.3
19
18
Exercise 2
With Outlier
92.6
98
90
Without Outlier
99.25
99
90
Looking at this table, we notice that the mode did not change when excluding the outlier. Let's now take a look at the differences between the mean and the median in Exercise 1.
Data set
Mean
Median
Exercise 1
With Outlier
22.8
19.5
Without Outlier
19.3
19
Difference
≈ 3.47
0.5
Let's do it for Exercise 2 as well.
Data set
Mean
Median
Exercise 2
With Outlier
92.6
98
Without Outlier
99.25
99
Difference
≈ 6.58
1
The mean is the measure of central tendency that is most affected by an outlier. This result is to be expected, because the mean depends on the sum of the data values. Including an outlier in the sum will affect the sum in a more noticeable way.
