What is the difference between mean, median, and mode?
Mean (arithmetic average) = sum of all values ÷ count of values. Median = the middle value when numbers are sorted; for even counts, it's the average of the two middle values. Mode = the most frequently occurring value. Example: for [2, 3, 3, 5, 7]: mean = 4.0, median = 3, mode = 3.
When should I use median instead of mean?
Use median when your data contains outliers that skew the average. For example, household income data: if most households earn $40,000–$80,000 but a few earn $5 million, the mean is misleadingly high. The median better represents the typical household. Real estate prices, salaries, and income distributions often use median for this reason.
Can I enter decimal numbers?
Yes. The calculator accepts integers, decimals (e.g. 3.14), and negative numbers. Separate values with commas, spaces, or line breaks.
Is this calculator free?
Yes — completely free with no signup required. All calculations run in your browser with no data sent to any server.
What is the range and why does it matter?
Range = maximum − minimum value. It measures the spread of your data. A mean of 80 from scores of 78–82 tells a very different story from scores of 50–100 that also average 80. Always report range alongside the mean to give context about variability.
Can a data set have no mode?
Yes. If every value in the dataset appears exactly once, there is no mode. Some datasets have multiple modes — called bimodal (two modes) or multimodal (three or more). For example, [1, 2, 2, 3, 3] has two modes: 2 and 3.
How do I calculate a weighted average?
A weighted average assigns different importance to values: Weighted mean = Σ(value × weight) ÷ Σweights. Example: a course where homework (40%) and exams (60%) have different weights — a 90 homework grade and 70 exam grade gives 0.4×90 + 0.6×70 = 36 + 42 = 78, not the arithmetic mean of 80.