Question

Unlike the mode or median, the mean is affected by

a) only those observations that are middle-ranked.
b) only those observations that occur most often.
c) all those observations that are extreme.
d) all observations.

Answer 1

The mean is affected by all observations in a data set, including extreme values or outliers. It is the measure of central tendency that is most sensitive to skewness, as its value can be greatly influenced by single outliers, unlike the more robust median and mode.

Step-by-step explanation:

Unlike the mode or median, the mean is affected by all observations, which includes extreme values or outliers. While the median represents a number that separates ordered data into halves, and the mode is the value that appears most frequently, the mean, which is the arithmetic average, is impacted by every single data point.

The mean is particularly sensitive when a data set is skewed, as it can be affected by even a single outlier more than the median or mode. Therefore, extreme observations in the data set can significantly affect the calculation of the mean, making it larger or smaller depending on the nature of these outliers. In contrast, the median and mode are more robust against such skewness since they are positional measures.

Moreover, when a distribution is symmetric, the mean and median are close together, near the mode which is the high point of the distribution. This often changes with skewed distributions, where the relationships among these measures of central tendency shift accordingly.