The measure of center that is most affected by outliers is the mean. Outliers have the potential to heavily skew the mean, as it takes into account the numerical values of all data points when calculating the average.
For example, let's consider the following data set:
10, 15, 16, 20, 22, 25, 30, 35, 40, 100
The mean of this data set is (10+15+16+20+22+25+30+35+40+100)/10 = 29.3
Now, let's add an outlier to the data set:
10, 15, 16, 20, 22, 25, 30, 35, 40, 100, 200
The new mean becomes (10+15+16+20+22+25+30+35+40+100+200)/11 = 47.3
As we can see, the addition of the outlier drastically increased the mean from 29.3 to 47.3. This demonstrates how outliers can significantly impact the mean, making it less representative of the data as a whole. In contrast, the median and mode are less affected by outliers since they are not as influenced by extreme 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.
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