An outlier is a data value that is much greater than or much less than the other values in a data set.
See solution.
Practice makes perfect
An outlier is a data value that is much greater than or much less than the other values in a data set. To find the outlier of a data set, it is always convenient to write the data in numerical order.
To describe how removing an outlier from a data set affects the mean, we will analyze two cases — one when the outlier is greater than the other values and one when it is less than the other values.
Greater Outlier
Recall that the mean is the sum of the data values divided by the number of data values. Let's look at some example data sets and how the mean changes by removing the outlier. We will also compare the mean with the median of the data.
As we can see, removing the outlier decreases the mean of the data set. Additionally, the mean gets closer to the median.
Lesser Outlier
In the same way, let's look at some data set examples when the outlier is less than the other values.
Similarly, the mean gets closer to the median. However, removing the outlier increases the mean.
Conclusion
If the outlier of the data set is much greater than the other values, removing it decreases the mean. Conversely, if the outlier is much less than the other values, removing it increases the mean. In both cases, the mean gets closer to the median.
