Measure of Central Tendency — Definition, Formula & Examples
A measure of central tendency is a single value that represents the "center" or typical value of a data set. The three most common measures are the mean (average), median (middle value), and mode (most frequent value).
A measure of central tendency is a summary statistic that identifies a central or representative value around which a set of data points tends to cluster. The arithmetic mean, median, and mode each use a different method to locate this central value, and the choice among them depends on the distribution and type of data.
How It Works
To find the mean, add all values and divide by the count. To find the median, sort the values and pick the middle one (or average the two middle values if the count is even). To find the mode, identify which value appears most often. For symmetric data, mean and median are usually close together. For skewed data or data with outliers, the median often gives a better sense of a typical value.
Worked Example
Problem: Find the mean, median, and mode of this data set: 3, 5, 5, 7, 10.
Mean: Add all values and divide by the number of values.
Median: The data is already sorted. With 5 values, the middle value is the 3rd one.
Mode: The value 5 appears twice, more than any other value.
Answer: The mean is 6, the median is 5, and the mode is 5.
Why It Matters
Measures of central tendency show up in science fair projects, news reports, and sports statistics whenever someone needs to summarize a group of numbers with one representative value. Understanding which measure to use helps you interpret data accurately — for example, median household income is reported instead of mean income because a few extremely high earners would skew the average.
Common Mistakes
Mistake: Always using the mean without checking for outliers.
Correction: Outliers can pull the mean far from most data points. When your data is skewed or contains extreme values, the median is usually a more representative measure of center.