ABCTE Professional Teaching Knowledge Practice Exam

Which measure of central tendency is described as more resistant to extreme values in a dataset?

1. Mean

2. Mode

3. Median

4. Standard deviation

The correct answer is: Median

The median is a measure of central tendency that represents the middle value in a dataset when it is ordered from least to greatest. It is particularly notable for its resistance to extreme values, or outliers, which can significantly distort the mean. When a dataset contains extreme high or low values, the mean can be skewed, leading to a less accurate representation of the central tendency. In contrast, the median remains stable regardless of how extreme the values are on either end. For example, in the dataset [1, 2, 2, 3, 100], the mean is affected by the extreme value of 100, resulting in a mean of 21.6, while the median is 2, which better reflects the central tendency of the majority of the values. This quality makes the median a more robust measure of central tendency in the presence of outliers, providing a clearer picture of the data's center. Other measures like the mode, which identifies the most frequently occurring value, and standard deviation, which measures the dispersion of the dataset, do not inherently focus on the central location in the same way the median does, making them less resistant to extreme values in this context.