Mean, Median, Mode, Range Calculator

This mean median mode range calculator computes the four core statistics from a single data set: Mean (x̄, arithmetic average), Median (x̃, middle value), Mode (Mo, most frequent value(s)), and Range (R, max − min). The Logic Trace shows sorting, the mean formula (Σx / n), a frequency map for mode, and the range calculation, so you get both quick answers and a clear view of how each number is found. It’s built for students checking homework, teachers explaining descriptive statistics, and anyone who needs to find the range of a data set, find mean with decimals, or calculate the median for an even number of values (average of the two middle values). Bimodal or multimodal data are supported: every value that ties for highest frequency is listed as a mode.

Four statistics, one data set. The mean (arithmetic average) uses : sum every value and divide by the count. The median is the middle value after sorting. When n is odd, it is the single center entry; when n is even, average the two middle values. The mode is found by counting how often each value appears (a frequency map) and selecting the value or values with the highest count. If no value repeats, there is no mode. Range measures spread: . As a worked example, consider the set {3, 7, 7, 12, 21}. Mean = 50 / 5 = 10. Median = 7 (the third of five sorted values). Mode = 7 (appears twice). Range = 21 − 3 = 18. The Logic Trace walks through these same four steps with your data.

Enter your numbers in the input area, comma-separated, space-separated, or one per line. You can also click Random sample to generate data or Load example to try presets like test scores or heights. Use the mean precision dropdown to round the mean to 0–5 decimal places, which is handy for reporting. Once you submit, the Result pane displays mean, median, mode, range, geometric mean, sum, and count. The sorted bar highlights Min (green), Max (red), and median position(s) (accent) so you can visually verify how median and range are derived. Below the results, the Logic Trace walks through each step: sorting the data, computing the sum and division for the mean, building a frequency map for the mode, and subtracting Min from Max for the range. Copy the results to your clipboard with one click.

These three describe where the “center” of the data lies, in different senses.

Mean (x̄): The arithmetic average. Sum all values and divide by the count. The mean is sensitive to outliers: one very high or low value can pull it away from the rest. Use it when you want the balance point of the numbers.

Median (x̃): The middle value when the data is sorted. If n is odd, it’s the single center value; if n is even, it’s the average of the two middle values (so calculating the median for an even number of values is straightforward: sort, then average the two middle numbers). The median is resistant to outliers and is often preferred for incomes, house prices, or any data where extremes can distort the average.

Mode (Mo): The value or values that appear most often. A set can be unimodal (one mode), bimodal (two values tie for highest frequency), or multimodal. If no value repeats, there is no mode. This calculator lists every value that has the maximum frequency.

Range (R) measures how spread out the data is: . You subtract the smallest value from the largest. It’s easy to compute and interpret, but it uses only two values, so one extreme can make the range large. To find the range of a data set, sort the values (or scan for min and max), then subtract. This calculator shows the sorted list and highlights Min and Max so you can see exactly how the range is found.

To find the mean by hand: (1) Add all numbers, including decimals, to get Σx. (2) Count how many there are: n. (3) Divide: You can round the result to a chosen number of decimal places. This tool’s Logic Trace shows the full sum and the division step so you can verify the result or follow along when learning how to find mean with decimals.