Which measure is affected by outliers when calculating the center of a data set?

The measure that is most influenced by outliers when calculating the center of a data set is the mean. The mean is calculated by summing all the values in a data set and dividing by the number of values. This approach means that extremely high or low values can significantly shift the mean in the direction of those outliers. For example, if most data points are clustered in a certain range and a few extremely high or low values are included, the mean may not accurately reflect the central tendency of the majority of the data.

In contrast, measures like the median and mode are less affected by outliers. The median, which is the middle value when the data is arranged in order, remains stable regardless of extreme values. Similarly, the mode, which is the value that appears most frequently in the data set, is primarily concerned with frequency and does not change unless the outliers themselves are frequent enough to become the mode.

The weighted mean, like the regular mean, takes into account the magnitude of each value but can also be affected by outliers if those outliers carry a substantial weight in the calculation. However, it is the regular mean that is typically highlighted for its sensitivity to extreme values. Thus, the mean is the correct answer because of its