The measure of center most affected by outliers is the mean. This is because the mean is calculated by adding up all the data values and dividing by the total number of data points. This can be heavily influenced by extreme values, or outliers, in the data set.
For example, consider the following set of data:
2, 4, 6, 8, 10, 12, 14, 16, 18, 100
The mean of this data set is:
(2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 100) / 10 = 18
However, the outlier value of 100 significantly skews the mean to a value that may not be representative of the majority of the data points.
In contrast, the median, or the middle value when the data is sorted, is less affected by outliers. In this example, the median would be 10, which is a more accurate representation of the middle value in the data set. Similarly, the mode, or the most frequently occurring value, would also be less affected by outliers, as it is not influenced by extreme values.
So, in summary, the mean is the measure of center most affected by outliers because it takes all data points into consideration when calculating, while the median and mode are more resistant to outliers.
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.
1 answer