Ontario Mathematics Proficiency Practice Test

The mean is the measure of central tendency that is most affected by outliers because it is calculated by taking the sum of all values and dividing by the number of values. When an outlier, which is a value significantly higher or lower than the rest of the data set, is present, it can disproportionately influence the sum, thereby skewing the mean. For example, if the data set consists of the numbers 2, 3, 4, 5, and 100, the mean would be calculated as (2 + 3 + 4 + 5 + 100) / 5, resulting in a mean of 22.8, which does not accurately reflect the center of the majority of the data.

In contrast, the mode, which reflects the most frequently occurring value in a data set, remains unchanged regardless of outliers, as does the median, which represents the middle value and is only affected when the outliers change the distribution of the data significantly. The range measures the difference between the highest and lowest values but does not provide a sense of the central tendency itself. Thus, the mean is particularly sensitive to extreme values, making it the central tendency measure most influenced by outliers.