Question

Which one of the following is not true of the mean?

a) always best describes the central tendency of a distribution
b) reappears, out of mathematical necessity, throughout statistics
c) serves as a key component in more complex statistical measures
d) emerges as a well documented measure to use when generalizing beyond small sets of observations

Answer 1

The correct answer is option a), 'always best describes the central tendency of a distribution'. The incorrect statement about the mean is that it always best describes the central tendency of a distribution.

Step-by-step explanation:

This statement is not true because the mean is not always the best measure of central tendency. In cases where a dataset has outliers or a skewed distribution, the median may be a better measure of the central tendency.

The mean is sensitive to extreme values, and its position can be distorted by outliers, making it unrepresentative of the majority of the data points. This is why the median, which is less affected by outliers and skewed data, might provide a clearer view of the dataset's central tendency. However, the mean does reappear throughout statistics (option b) as it serves as a foundational element in many statistical measures (option c) and can be useful when generalizing beyond small sets of observations (option d), assuming the distribution is well-behaved and not heavily skewed or containing outliers.