Central tendency measures are statistical tools that help us understand the typical or central value in a dataset. The three main measures are the mean, which is the average of all values, the median, which is the middle value when data is ordered, and the mode, which is the most frequently occurring value. These measures are essential for analyzing data in various contexts like economics, education, and sports.
The mean, also called the average, is calculated by adding all values in a dataset and dividing by the number of values. For example, if we have test scores of 85, 90, 78, 92, and 88, we add them to get 433, then divide by 5 students to get a mean of 86.6. The mean is useful because it considers all values in the dataset, but it can be affected by extremely high or low values called outliers.
The median is the middle value when data is arranged in ascending or descending order. To find the median, first order the data from smallest to largest. If there's an odd number of values, the median is the middle value. If there's an even number of values, the median is the average of the two middle values. For example, with heights 158, 162, 165, 170, and 175 centimeters, the median is 165 because it's the middle value of the five ordered values.
The mode is the value that appears most frequently in a dataset. Unlike the mean and median, the mode can be used with categorical data like colors or names. A dataset can have one mode, called unimodal, two modes called bimodal, or multiple modes called multimodal. Some datasets have no mode when all values appear with the same frequency. In our example of favorite colors, blue appears three times, making it the mode of this dataset.