Which measure is least affected by extreme values in a dataset?

Which measure is least affected by extreme values in a dataset?

• A. The mean
• B. The mode
• C. The standard deviation
• D. The median

Answer: (D)

The median is the measure that is least affected by extreme values in a dataset because it is defined as the middle value when all the numbers are arranged in ascending or descending order. In other words, the median represents the point at which half the values lie below and half lie above, making it a robust indicator of central tendency. When extreme values, or outliers, are present in a dataset—whether they are particularly high or low—the mean can be significantly skewed in the direction of those outliers. The standard deviation, which measures the amount of variation or dispersion of a set of values, can also be heavily influenced by extreme values since it uses the mean as a reference point. The mode, while it can be somewhat unaffected, is a tally of the most frequently occurring value(s) in the dataset but may not accurately represent the overall distribution if there are extreme values. By focusing on the positions of values rather than their magnitudes, the median maintains a more stable measure of central location, thus making it less susceptible to distortions caused by extreme values.

The median is the measure that is least affected by extreme values in a dataset because it is defined as the middle value when all the numbers are arranged in ascending or descending order. In other words, the median represents the point at which half the values lie below and half lie above, making it a robust indicator of central tendency.

When extreme values, or outliers, are present in a dataset—whether they are particularly high or low—the mean can be significantly skewed in the direction of those outliers. The standard deviation, which measures the amount of variation or dispersion of a set of values, can also be heavily influenced by extreme values since it uses the mean as a reference point. The mode, while it can be somewhat unaffected, is a tally of the most frequently occurring value(s) in the dataset but may not accurately represent the overall distribution if there are extreme values.

By focusing on the positions of values rather than their magnitudes, the median maintains a more stable measure of central location, thus making it less susceptible to distortions caused by extreme values.