How the mean median mode calculator works
Paste your list and the calculator finds all three averages at once: the mean (add everything, divide by the count), the median (sort the list, take the middle), and the mode (the value that appears most often). It also gives you the range, the midrange, the count, the sum, and a full frequency table showing each distinct value with its count, its relative frequency as a decimal and a percent, and the cumulative count. Every result comes with its working shown, using your own numbers, so you can follow the arithmetic rather than trust a box.
If you just want a quick everyday average, our average calculator is the lighter tool: mean and median without the ceremony. This page is the stats-class version. It adds the mode with all its edge cases handled honestly (two modes, no mode), the midrange, and the frequency table that makes the mode visible instead of just announced.
The formulas
The mean uses every value. The median uses only the sorted order. The mode uses only the counts. That is why they can disagree, and why the disagreement is often the most interesting number on the page.
Worked example
Five people work at a small shop. Their salaries are $38,000, $42,000, $42,000, $45,000, and $250,000 (the last one is the owner).
Mean: the salaries sum to $417,000, and $417,000 / 5 = $83,400. That is higher than what four of the five people actually earn.
Median: sorted, the middle value is $42,000. Half the staff earn at or below it, half at or above it.
Mode: $42,000 appears twice, more than any other salary, so the mode is $42,000: the most common paycheck in the room.
Range: $250,000 - $38,000 = $212,000. Midrange: ($250,000 + $38,000) / 2 = $144,000, which nobody earns; it is fragile for exactly this reason.
Three averages, because one number cannot hold a shape
All three answers in the example are correct, and they differ by a factor of two. That is not a flaw in the arithmetic; it is the whole reason three averages exist. The mean chases the outlier, because every dollar pulls on it. The median stays with the middle person, because sorting puts the outlier at the end of the line where it counts as just one entry. The mode reports the common case, the answer you would get by asking around the room. One data set, three honest summaries, three different questions answered.
This is why the choice of average matters whenever numbers reach the public. Home prices are reported as medians because a few mansions would otherwise drag the figure above what a typical buyer pays. Average salary claims often use the mean, which is the right number for total payroll and a misleading one for what a typical employee takes home. Neither number is dishonest; each answers a different question. The useful habit, and the one this page is built to teach, is asking which question a quoted average is answering before you let it persuade you. When someone hands you an average, it is fair to ask: mean or median?
A good second habit: check the gap. When the mean and median land close together, the data is usually roughly symmetric. When the mean sits well above the median, something large is pulling it up (a right skew); well below, something small is pulling it down. This calculator runs that check on your data automatically and says what it sees in plain words. And once you know where the middle of your data is, the natural next questions are how spread out it is (the standard deviation and variance calculators) and where a particular value stands within it (the percentile and quartile calculators).