Final answer:
The measures of the center of distribution are the mean and the median. The mean is preferred when the data is relatively symmetric, as it provides an accurate measure when there are no extreme values or outliers. However, for skewed distributions or when outliers are present, the median is more appropriate as it is unaffected by extreme values.
Step-by-step explanation:
The two most commonly used measures of the center of a distribution are the mean and the median. The mean, often referred to as the average, is calculated by summing all data points and dividing by the number of points. It is the most common measure of the center, and it is preferred when the data set is symmetric without outliers. The condition under which the mean is preferred can be described as: (A) The mean is preferred when the data is relatively symmetric. This is because the mean can be heavily influenced by extreme values or outliers, making it an inaccurate measure of central tendency for skewed distributions. On the other hand, the median, which is the middle value that divides the data set into two equal halves, is not affected by the extreme values. Therefore, the median is a better measure when a data set contains outliers or is heavily skewed.
The mode, another measure of central tendency, is the most frequently occurring data point in the data set. While it is useful in certain contexts, it is not a measure of central tendency that represents the center of a dataset as effectively as the mean or median under most conditions.
The mean should not be used when the data is strongly skewed or has outliers, for such distributions, the median is often more representative of the data's central tendency. Also, the preference for the mean does not depend on whether there are few or many data points; rather, it depends on the symmetry of the distribution.