Mean Median Mode Calculator

Four quick definitions. Mean = sum of values divided by count. Median = middle value after sorting. Mode = most frequent value. Range = maximum minus minimum. Take {3, 5, 7, 7, 8, 10, 12}. Mean = 52/7 ≈ 7.43. Sorted, the middle value (4th) is 7, so median = 7. The number 7 appears twice — that's the mode. Range = 12 − 3 = 9. Together these four give a quick portrait of centre and spread, especially useful before any deeper statistical analysis.

Add up all your numbers, then divide by how many there are. That's it. For values like {4, 8, 6, 10, 7}, sum = 35, count = 5, mean = 35/5 = 7. Most calculators accept input separated by commas or spaces — paste your data, hit calculate, and you get the answer. Watch out for two things: missing values can throw off your count, and one extreme outlier can shift the mean noticeably. For skewed data with outliers, the median is often a more honest measure of centre.

With an even count of values, there's no single middle, so you take the two middle values and average them. Sort first. For {3, 5, 8, 12, 14, 18}, n = 6, so the 3rd and 4th values are 8 and 12. Median = (8 + 12)/2 = 10. Always sort before locating the middle — students often forget that step. The general rule: with n values, the median position for odd n is (n+1)/2; for even n, it's the average of positions n/2 and n/2 + 1.

If every value appears exactly once, your dataset has no mode by the most common convention. Some textbooks and calculators still report "no mode" or treat all values as modal, but most just say no mode exists. For example, {2, 5, 7, 11, 14} has no repeats and therefore no mode. This often happens with continuous data or small samples. When no mode exists, lean on the mean and median to describe centre instead — they're usually more informative for non-categorical data anyway.

Yes, definitely. If two values tie for most frequent, the data is bimodal; three or more ties make it multimodal. Take {2, 4, 4, 6, 7, 7, 9}: both 4 and 7 appear twice, so the modes are 4 and 7. List them all rather than picking one — bimodal patterns often signal that your data comes from two distinct groups (say, heights of men and women combined). Mode plays a particularly important role with categorical data, where mean and median don't apply.

The median is the safer choice for skewed data. Because the mean adds up every value, a long tail of large or small numbers drags it in that direction, making it unrepresentative. The median, sitting at the middle position, isn't pulled around by extreme values. House prices are the classic example: a few mansions can push the mean well above what a typical home costs, while the median stays close to the typical price. Use the mean for symmetric, outlier-free data; use the median when the distribution is skewed.

The mean is the most sensitive — it adds up every value, so a single extreme number drags it noticeably. The median is far more resistant, since it only depends on rank, not magnitude. The mode is essentially unaffected unless the outlier happens to repeat. Take {2, 4, 6, 8, 10}: mean = 6, median = 6. Add an outlier of 100: mean jumps to about 21.7, but the median only nudges to 7. That's why the median is preferred for income data, exam outliers, and other skewed real-world distributions.

Subtract the minimum value from the maximum: range = max − min. For {12, 18, 25, 7, 31}, max = 31, min = 7, so range = 24. Quick and simple, but the range only uses two values, ignoring everything in between. That makes it sensitive to outliers — one unusually high or low data point inflates the range dramatically. For a more robust view of spread, use the IQR (Q3 − Q1) or the standard deviation, both of which account for more of the data.