Mean, Median, Mode and Range Calculator

What each statistic tells you

Mean, median, mode, and range describe a list from different angles. The mean is the arithmetic average: add every value and divide by the count. The median is the middle after sorting. The mode is the value that occurs most often. The range is the largest value minus the smallest.

Enter scores, prices, measurements, or any other numeric list. The calculator accepts commas, spaces, semicolons, and line breaks. It skips empty entries and reports the count and sum so you can audit the result. These measures are descriptive, not a judgment about whether a result is good.

The mean uses every observation, so an extreme value can move it. The median uses position, so it often represents a typical observation better when a list has a long tail. A mode can be useful for repeated categories such as shoe sizes, but a list with unique values has no mode. Range shows spread, although it does not reveal how values are clustered between the endpoints.

Before calculating, decide what one row means. If the list contains one score per assignment, an unweighted mean gives each assignment equal influence. If one row summarizes a class of 30 students and another summarizes a class of 10, averaging those two class percentages gives each class equal influence rather than each student. Keep the unit of observation consistent.

Missing values need the same care. A blank cell should usually be left out, while a recorded zero should stay in the list. Replacing a missing value with zero lowers the mean and changes the count. Replacing it with the mean hides uncertainty. Record how many observations were available so another person can reproduce the summary.

Finally, keep the raw list alongside the summary. A future reader can sort it, check a repeated value, and see whether the result includes the same population. Four statistics are useful signposts, but the data behind them remains the evidence.

Worked example: six scores

Consider six scores: 78, 85, 92, 88, 71, and 95. Their sum is 509 and the count is 6, so the mean is 509 divided by 6, or 84.83. Sort them as 71, 78, 85, 88, 92, and 95. With an even count, the median is the average of the two middle values: (85 + 88) / 2 = 86.5.

The highest score is 95 and the lowest is 71, so the range is 24. Every score appears once, so there is no mode. The mean is below the median because the low score of 71 pulls the sum down more than the high score of 95 pulls it up.

If the list has an odd count, the median is one value rather than two. Remove 71 and the five remaining scores have a median of 88. Their sum is 438, so their mean is 87.6. The different answers are both correct because they describe different lists.

Rounding is best done at the end. For the six-score example, 509 / 6 gives 84.8333..., which displays as 84.83. If you round each score first or round an intermediate total, small differences can accumulate. Keep full precision for calculations, then choose a sensible number of decimal places for the report.

Units matter too. Do not combine miles with kilometers, dollars with cents, or temperatures in Fahrenheit and Celsius without converting first. A calculator can faithfully summarize inconsistent numbers, but its result will still be misleading. Add the unit to the label or keep separate lists when the measurements are not comparable.

Outliers and the choice of center

Add a score of 40 to the original list. The new sum is 549 and the count is 7, so the new mean is 549 / 7 = 78.43. The sorted list is 40, 71, 78, 85, 88, 92, 95, and the middle value is 85. One low observation moved the mean 6.40 points but moved the median only 1.50 points.

This is why median is common for home prices and incomes. A few unusually large values can make an arithmetic mean look higher than what a typical person encounters. Mean is still the right choice when every observation should contribute equally, such as total points earned across equally weighted assignments.

Do not remove an outlier only because it changes the answer. First ask whether it is an error, a rare but valid event, or the observation you care about. A manager planning staffing may need the mean demand, while a resident asking what a typical bill looks like may prefer the median.

Mode and repeated values

The mode is a frequency measure. In the list 2, 4, 4, 6, 8, 8, 8, the mode is 8 because it appears three times. A list may have two modes when two values tie for the highest frequency. It may have no mode when all values appear once.

Mode works with labels as well as numbers. If a store records small, medium, medium, large, and medium, medium is the most common size even though there is no meaningful arithmetic mean of the labels. For numeric data, mode can reveal a repeated price or a common response that the mean and median hide.

Be careful with rounded measurements. Values such as 10.0 and 10.00 are the same numeric value, while 10.0 and 10.1 are different. The widget treats exact numeric matches as repeats. It does not create bins, round inputs before counting, or infer a mode from nearby measurements.

Range, spread, and limits

Range is easy to calculate and easy to overread. Subtract the minimum from the maximum. For the six scores, 95 - 71 = 24 points. It tells you the full width of the observations, but one unusual endpoint can make the range look large. It also says nothing about whether the other values sit close together or are evenly spaced.

For a fuller view, compare range with the mean and median, then inspect the values themselves. A list of 1, 2, 3, 4, and 100 has a range of 99, mean of 22, and median of 3. The median exposes the typical position, while the mean reflects the large value. For a list such as 18, 19, 20, 21, and 22, the range is 4 and both centers are 20.

When a decision matters, keep the original list and record whether values were rounded, filtered, or measured under different conditions. A clean summary cannot fix inconsistent input.

Averages, rates, and percentages

Do not average percentages without their denominators. Suppose one store has 5 sales from 100 visitors and another has 90 sales from 900 visitors. The simple mean of 5% and 10% is 7.5%, but the combined result is 95 sales out of 1,000 visitors, or 9.5%. The larger store has nine times the traffic, so it deserves nine times the weight.

The same issue appears with test results from classes of different sizes, average order rates, and conversion dashboards. Add the underlying counts and divide once when you can. If you only have percentages and no denominators, label a plain average as an unweighted summary rather than calling it the combined rate.

Sequential percentage changes are another trap. A $100 balance that falls 50% becomes $50, then rises 50% to $75. The two changes average to zero percentage points, but the balance is still down 25%. Use the measure that matches the question.

A real-world median example

The U.S. Census Bureau reported real median household income of $83,730 for 2024, compared with $82,690 in 2023, in its 2024 income report. Median means half of households were above that midpoint and half below it. It does not mean every household earned $83,730, and it is not interchangeable with an average.

The Census Bureau uses median income because income distributions are uneven. A small number of very high incomes can pull the mean upward, while the median stays at the midpoint of households. Read the population, year, inflation basis, and income definition before comparing a statistic with another source. The Census Bureau income report explains those details.

For more background, the NIST handbook entry on measures of location explains why mean, median, and mode answer different questions. These references help you choose a summary rather than treating one statistic as universally best.

When comparing groups, report the sample size beside the statistic. A median of 86.5 from 6 scores carries less information than the same median from 600 scores. Small lists can change sharply when one observation is added. A useful report might say “median 86.5, n = 6, range 24” instead of presenting 86.5 alone.

For repeated tracking, use the same rule each time. Decide whether late submissions, canceled orders, or zero-demand days count before you inspect the result. Consistent definitions make a month-to-month comparison meaningful. If the definition changes, note the change next to the new mean or median.

Reading the result carefully

A summary is useful only when the input and the question match. A mean of dollars per order cannot answer a question about typical household income, and a median from six records should not be presented with the same confidence as a median from six thousand records.

Use count beside every reported statistic. Check whether values are independent, whether repeated values are real, and whether one extreme value is an error. If the source rounds numbers, keep that fact in the note. For recurring reports, keep the same definitions and sorting rules.