What's the difference between mean, median, and mode?

Mean is the arithmetic average (sum divided by count). Median is the middle value when numbers are ordered (or average of two middle values). Mode is the most frequently occurring value. Each measure has different uses: mean for overall trends, median for central tendency resistant to outliers, and mode for most common occurrences.

When should I use median instead of mean?

Use median when your data has outliers or is skewed. For example, in income data, a few extremely high salaries can inflate the mean, making median a better representation of 'typical' income. Median is robust against extreme values and better represents the center of skewed distributions.

Can a dataset have more than one mode?

Yes! A dataset with two modes is bimodal, three modes is trimodal, and more than three is multimodal. If all values appear with equal frequency, there's no mode. If no value repeats, the dataset has no mode. Multiple modes often indicate distinct groups or patterns within your data.

How do you calculate the mean of grouped data?

For grouped data (frequency distributions), multiply each value by its frequency, sum these products, then divide by the total frequency. For example, if you have three 5's, two 8's, and one 10: mean = (3×5 + 2×8 + 1×10)/(3+2+1) = 41/6 ≈ 6.83.

What is a weighted average and how is it different?

A weighted average assigns different importance (weights) to different values. Instead of sum/count, use (value₁×weight₁ + value₂×weight₂ + ...)/(weight₁ + weight₂ + ...). Common in grade calculations where tests count more than homework, or in financial portfolios where different investments have different sizes.

Math

Average Calculator

Calculate mean, median, and mode.

How to Use This Calculator

Enter your data set

Input all numbers in your dataset, typically separated by commas, spaces, or line breaks. You can enter as many values as needed. The calculator accepts decimals, negative numbers, and repeated values.

Select calculation type

Choose whether you want to calculate mean, median, mode, or all three (recommended). Some calculators also offer additional statistics like range, sum, and count.

Interpret the results

Review all calculated measures of central tendency. The calculator shows mean, median, and mode along with the sorted dataset for median verification. Understanding all three measures gives a complete picture of your data's central tendency.