The measure of center that is most affected by outliers is the mean. This is because the mean is calculated by adding up all of the data points and dividing by the total number of data points. Outliers can have a significant impact on the sum of the data points and therefore skew the mean.
For example, let's consider the following dataset with 10 data points:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
The mean of this dataset is (2+4+6+8+10+12+14+16+18+20) / 10 = 10.
Now, let's consider if we add an outlier to this dataset:
2, 4, 6, 8, 10, 12, 14, 16, 18, 100
The mean of this new dataset is (2+4+6+8+10+12+14+16+18+100) / 10 = 18.
As we can see, the outlier of 100 greatly affects the mean of the dataset, pulling it higher. In comparison, the median and mode of the dataset will remain the same (10 and no mode, respectively), regardless of the presence of the outlier.
Of the mean median and mode which measure the center is most affected by outlanders explain your reasoning including example with at least 10 data set points with 10 data points
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