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Mean, Median, Mode, Range, and Weighted Average Explained

"Average" is a word people use loosely, but in statistics it can refer to several different measures, each of which describes a data set in a different way. Mean, median, and mode are the three main measures of central tendency, while range describes how spread out the data is. Weighted average adds another layer, accounting for the fact that not every number in a data set necessarily deserves equal importance. This guide breaks down all five, with examples for each.

Mean: The Everyday "Average"

The mean is what most people mean when they say "average." It's calculated by adding up every number in the set and dividing by how many numbers there are.

Example: For the numbers 12, 15, 18, 15, 20, 9, the sum is 89, and there are 6 numbers. Mean: 89 ÷ 6 = 14.83.

The mean is useful for most everyday purposes, but it's sensitive to outliers. A single very large or very small number can pull the mean significantly away from where most of the data actually sits.

Median: The Middle Value

The median is the middle number when all values are sorted in order. If there's an even count of numbers, the median is the average of the two middle values.

Example: Sorting 12, 15, 18, 15, 20, 9 gives 9, 12, 15, 15, 18, 20. With 6 numbers, the median is the average of the 3rd and 4th values: (15 + 15) ÷ 2 = 15.

The median is far less affected by outliers than the mean, which is why it's often the better choice for describing typical values in skewed data, like household income or home prices, where a few extremely high values would otherwise distort the mean.

Mode: The Most Frequent Value

The mode is simply the number (or numbers) that appear most often in the data set. A set can have one mode, multiple modes (if there's a tie), or no mode at all (if every value appears exactly once).

Example: In 12, 15, 18, 15, 20, 9, the number 15 appears twice, more than any other value, so the mode is 15.

Mode is especially useful for categorical or non-numeric data, like finding the most common shoe size sold or the most frequent response in a survey, where mean and median don't make sense to calculate.

Range: How Spread Out the Data Is

Range measures the spread between the smallest and largest values in a data set, giving a quick sense of how much variation exists.

Example: For 12, 15, 18, 15, 20, 9, the maximum is 20 and the minimum is 9. Range: 20 − 9 = 11.

A small range means the data is tightly clustered together. A large range means there's significant variation, which can be a signal worth investigating further, especially in quality control or performance tracking.

Weighted Average: When Not Every Number Counts Equally

A simple mean treats every number the same, but that's often not realistic. A final exam might count for more of a grade than a quiz, and different investments in a portfolio carry different amounts of money. Weighted average accounts for this by multiplying each value by its weight before averaging.

Example: A student scores 85, 90, 78, and 92 on four assignments, worth 20%, 20%, 30%, and 30% of the final grade respectively. Weighted sum: (85×20) + (90×20) + (78×30) + (92×30) = 1,700 + 1,800 + 2,340 + 2,760 = 8,600. Total weight: 20+20+30+30 = 100. Weighted average: 8,600 ÷ 100 = 86.

Notice this differs from the simple mean of the same four scores, which would be (85+90+78+92) ÷ 4 = 86.25. The weighted average correctly reflects that the two 30%-weighted assignments (78 and 92) had more influence on the final result than the two 20%-weighted ones.

Which Measure Should You Use?

Use the mean for a quick, general summary when your data doesn't have extreme outliers. Use the median when outliers could distort the picture, like income or property prices. Use the mode when you care about the single most common value, especially with categorical data. Use range to understand variability at a glance. And use weighted average whenever different data points genuinely carry different levels of importance, such as grades, investment portfolios, or survey responses weighted by sample size.