Explain the difference between mean, median, and mode. When would you use each measure of central tendency?

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Accepted Answer

Mean, median, and mode are three fundamental measures of central tendency that help describe the center of a dataset. Each has specific use cases depending on the data distribution and analysis goals.

The mean is the arithmetic average, calculated by summing all values and dividing by the count. It uses every data point in the calculation, making it sensitive to all values. For example, in the dataset [2, 3, 4, 5, 6], the mean is 4. The mean works best when data is symmetrically distributed without extreme outliers. Use it for normally distributed data like test scores or heights in a population.

The median is the middle value when data is sorted in order. For odd-sized datasets, it is the center value. For even-sized datasets, it is the average of the two middle values. In the dataset [2, 3, 4, 100, 200], the median is 4, while the mean would be 61.8. The median is robust to outliers and extreme values. Use it when data is skewed, such as income distributions or house prices, where a few very high values would distort the mean.

The mode is the most frequently occurring value in a dataset. In [1, 2, 2, 3, 4], the mode is 2. A dataset can have no mode, one mode, or multiple modes. The mode is particularly useful for categorical data where calculating a mean is not meaningful. Use it for finding the most popular product category, the most common customer segment, or the peak hours of website traffic.

In practice, examining all three measures together provides a fuller picture of your data. When mean and median are close, the data is likely symmetric. When the mean is higher than the median, the data is right-skewed. When the mean is lower than the median, the data is left-skewed.