How can we use the concept:
Outliers are identified by the fact that they don’t follow the general trend of the data.
On a scatter plot, the point would not match the general trend of the rest of the data. Data sets can have no outliers, one outlier or multiple outliers.
When looking at a set of data, the outlier is much higher or lower than the rest of the data set.
Sample Math Problems
1. Study the plot and identify the outlier.
Solution: Point G is the outlier. The rest of the plotted points are in a positive general trend. Points E and F are included in this general trend.
2. If the outliers are removed from the plot, determine whether the association between the two variables is positive or negative.
Solution: Points R and S are outliers because they do not follow the general trend. If they are removed, the association is a negative trend.
3. Identify the outlier in the following set of data: 5 9 4 8 87 6
Solution: The number 87 is the outlier. It is much higher than the other data points.
4: Find the outlier and tell how it affects the mean for the following set of data.
50 64 52 63 62 10 59 54
Solution:
Solution:
The number 10 is the outlier because it is much lower than the other data points.
Calculate the mean with the outlier and without the outlier by adding all the numbers together and dividing by the number of data points.
With Outlier: Add 50+64+52+63+62+10+59+54 = 414
Then, divide 414 by 8 = 51.75
Without Outlier: Add 50+64+52+63+62+59+54 = 404
Then, divide 404 by 7 = 57.71
Find the difference between the two means: 57.71 - 51.75 = 5.96
By eliminating the outlier the mean is raised by 5.96 and is a better representation of the data set.
