In descriptive statistics, which of the following

Solution

The median is the middle value in a dataset when the values are arranged in ascending or descending order. Unlike the mean, which can be heavily influenced by extreme values or outliers, the median is much less sensitive to such values. Outliers can skew the mean significantly, but the median remains unaffected because it is based on the position of the values rather than their magnitude. This makes the median a more reliable measure of central tendency in datasets with outliers. For example, in income data where a few high-income individuals distort the mean, the median provides a better representation of the typical value. Why Other Options Are Incorrect: • A: The mean is highly sensitive to extreme values. A single outlier can significantly alter its value. • C: The mode represents the most frequent value in the dataset and can be skewed if outliers occur frequently, though it is less sensitive than the mean. • D & E: Both variance and standard deviation measure the spread or dispersion of the data, and they are highly affected by outliers since they are based on squared deviations from the mean. Extreme values increase the variance and standard deviation.