Measures of Central Tendency

Measures of central tendency provide a summary of a set of data by describing the "typical" data point. The three most common measures are the mean, median, and mode.

Mean

The mean, often called the average, is calculated by adding up all the values in the dataset and then dividing by the number of values. The formula is:

Mean = Sum of all values / Number of values

Median

The median is the middle value in a dataset when the values are arranged in ascending (or descending) order. If the dataset has an odd number of observations, the median is the middle number. If the dataset has an even number of observations, the median is the average of the two middle numbers.

Mode

The mode is the value that appears most frequently in a dataset. A dataset may have one mode, more than one mode, or no mode at all.

Comparing the Measures

The mean, median, and mode are all measures of central tendency, but they highlight different aspects of the dataset:

  • The mean is influenced by every value in the dataset, including outliers. If there are extreme values, the mean may not be a representative measure of the center.

  • The median is not affected by outliers or extreme values, making it a better measure when a dataset is skewed or has outliers.

  • The mode can be used for both numerical and categorical data. It can be useful when the most common item is of interest.