The measure of center most affected by outliers is the mean. The mean is calculated by adding up all the values in the data set and dividing by the total number of values. Because the mean takes into account the magnitude of all values, even a single outlier can significantly skew the mean.
For example, let's consider the following data set with 10 values: 2, 3, 4, 5, 6, 7, 8, 9, 10, 100. The mean of this data set is:
(2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 100) / 10 = 15.4
The outlier in this data set is the value 100, which is much larger than the other values. As a result, the mean is significantly higher than the majority of the values in the data set. If we were to remove the outlier and recalculate the mean, we would get:
(2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) / 9 = 5.67
In this case, the mean value changes significantly when the outlier is removed, demonstrating how outliers can strongly impact the mean. In comparison, the median and mode are less affected by outliers because they are based on the middle value and the most frequent value, respectively, rather than the sum of all values.
Of the mean, median, and mode, which measure of center is most affected by
outliers? Explain your reasoning including an example with at least 10 data points.
(4 points)
3 answers
little shorter?
The measure of center most affected by outliers is the mean. The mean is calculated by adding up all the values in the data set and dividing by the total number of values. Because the mean takes into account the magnitude of all values, even a single outlier can significantly skew the mean.
For example, in a data set with values 2, 3, 4, 5, 6, 7, 8, 9, 10, and 100, the mean is greatly influenced by the outlier 100. The mean with the outlier included is 15.4, but without the outlier, it is 5.67. This demonstrates how outliers can strongly impact the mean. On the other hand, the median and mode are less affected by outliers since they are based on the middle value and the most frequent value, respectively, rather than the sum of all values.
For example, in a data set with values 2, 3, 4, 5, 6, 7, 8, 9, 10, and 100, the mean is greatly influenced by the outlier 100. The mean with the outlier included is 15.4, but without the outlier, it is 5.67. This demonstrates how outliers can strongly impact the mean. On the other hand, the median and mode are less affected by outliers since they are based on the middle value and the most frequent value, respectively, rather than the sum of all values.
3 answers