The measure of center that is most affected by outliers is the mean. This is because the mean is calculated by taking the sum of all values in the data set and dividing by the number of values, meaning that outliers have the potential to greatly skew the average.
For example, let's consider the following data set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 100.
The mean of this data set is calculated as:
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 100) / 10 = 14.5
In this case, the mean is significantly higher than the majority of the data points due to the outlier value of 100. This can give a misleading representation of the central tendency of the data set.
On the other hand, the median is calculated by finding the middle value of an ordered data set, and the mode is the most frequent value in the data set. These measures are not as heavily influenced by outliers because they are not affected by extreme values as much as the mean.
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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