The measure of center that is most affected by outliers is the mean. This is because the mean is calculated by adding up all the data points and dividing by the number of data points, so outliers can significantly skew the average.
For example, let's consider the following data set:
1, 2, 3, 4, 5, 6, 7, 8, 9, 100
The outliers in this data set are the number 100. If we calculate the mean of this data set, the sum of all the data points is 145. Dividing by 10 (the number of data points) gives us a mean of 14.5. However, the presence of the outlier 100 significantly inflates the mean, making it much higher than the actual central tendency of the data set.
On the other hand, the median and mode are less affected by outliers. The median is the middle value when all the data points are arranged in ascending order, while the mode is the value that appears most frequently. In this example, the median is 5.5 and the mode is not affected at all, remaining as 1.
In summary, outliers have a greater impact on the mean than on the median and mode because the mean takes into account the magnitude of the data points and their distance from the center.
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
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1 answer