Mean, Median, Mode, Range Calculator

Search engines see a single cluster of queries: “mean median mode calculator,” “mean median mode range,” “find the average median and mode.” This page is that cluster. Paste a list and read four headlines - mean, median, mode, range - plus the supporting count, sum, min, and max. There is no weight column. A weighted mean is a different search intent and lives on the average calculator.

Default data 4, 8, 6, 5, 3, 8 sorts to 3, 4, 5, 6, 8, 8. Sum = 34, n = 6, mean = 34/6 = 5.6̅ which displays as 5.667 to three decimals. Median is the average of the 3rd and 4th ordered values: (5 + 6)/2 = 5.5. Mode is 8 (frequency 2). Range is 8 − 3 = 5. Those four numbers are what a middle-school worksheet usually wants in one box.

When the assignment grows into quartiles, IQR, and two flavors of standard deviation, switch to the statistics calculator. When the assignment is only “find s or σ,” use the standard deviation calculator. Keeping this URL focused on the four-pack avoids stuffing every descriptive formula into the same H1.

1. Paste values separated by commas, spaces, semicolons, or new lines.
2. Read the four tiles. Mean uses every point equally. Median uses the ordered middle. Mode lists every value that ties for highest frequency. Range is max minus min.
3. If every observation is unique, mode reads no unique mode instead of naming the whole list as modes.
4. Copy the block, clear the box, or open fullscreen. The list stays in localStorage for 30 days on this device only.

Mean. Add the numbers. Divide by how many there are. Outliers pull it. It is the estimator that variance is built from, and it is usually what a prompt means by “average.”

Median. Sort. If n is odd, take position (n+1)/2. If n is even, average the two central positions. Half the ordered sample is on each side (ties on the value itself notwithstanding). One wild point cannot drag it past the neighboring order statistic.

Mode. The most common value. A list can have one mode, two (bimodal), or several (multimodal). If the maximum frequency is 1, this calculator reports no unique mode rather than calling a uniform list “every point is a mode,” which is true in a vacuous sense and useless on a worksheet.

Range. Only two points enter the formula. That makes it simple and fragile. Stretch the largest value and the range follows; the median may not move at all.

Incomes, listing prices, and city travel times are classic median territory: a handful of extreme observations inflate the mean until it describes nobody. A company that reports “average salary” of $180k because two executives make millions, while most staff earn $55k, is using the mean as marketing. The median would sit near $55k.

The mean still wins for symmetric lab measurements, for anything you will later plug into a variance or a z-score, and for totals: the mean times n recovers the sum, which the median does not. If a chemist averages three titration volumes, the mean is the right combiner. If a journalist describes typical rent in a city, the median is usually the honest headline.

Skew: a right tail (mean > median) is common for amounts of money and waiting times. A left tail (mean < median) shows up in exam scores piled against 100%. Mode can sit at a peak that is neither the mean nor the median - a bimodal class with a cluster of 40s and a cluster of 90s has two modes and a mean in the deserted middle.

Example: 2, 2, 5, 5, 9. Frequencies of 2 and 5 both equal 2, which beats 9. The tool lists 2, 5 (bimodal). Add another 9 and it becomes unimodal at a three-way conversation - actually 2, 5, 9 would then all have frequency 2, which is multimodal (three modes). There is no secret tie-break that prefers the smaller number; every winner is printed.

Continuous data rounded to the same bin can create a fake mode. If every height is recorded to the nearest centimeter, a spike at 170 cm may only reflect rounding. The calculator takes the numbers as typed; it will not re-bin for you.

In casual English, average means the arithmetic mean. In statistics, mean, median, and mode are all averages (measures of central tendency). A homework line that says “find the average” almost always wants sum / n. A line that says “find the average, the median, and the mode” wants this four-pack.

Weighted means appear when a 40% exam and a 60% project should not count equally, or when combining group means of different sizes. Those products of value × weight are the average calculator. Putting a weight box here would steal that query and confuse the four-pack layout. Likewise, sample versus population SD would steal the standard deviation query. Quartiles belong on statistics.

Odd n: 1, 4, 9. Mean = 14/3 ≈ 4.667. Median = 4. No unique mode. Range = 8. Even n with a clean middle: 10, 20, 30, 40. Mean = 25, median = 25, no unique mode, range = 30. All identical: 7, 7, 7. Mean = median = mode = 7, range = 0.

Negative values are allowed: −4, −1, 0, 2. Mean = −0.75, median = (−1+0)/2 = −0.5, no unique mode, range = 6. The mean is not “always bigger than the median”; sign and skew decide.

Large n from a CSV column can be pasted directly if the delimiter is comma, space, or newline. Ten thousand values is the cap so a phone browser is not asked to sort a million rows. For a population SD on that paste, use statistics or the SD tool - this URL will not grow extra rows of variance just to look complete.

Averaging two class means of 70 and 90 is 80 only if the classes have the same size. Thirty students at 70 and ten at 90 have overall mean (30×70 + 10×90)/40 = 75. That is a weighted mean, which this four-pack will not compute unless you expand the list to forty numbers. Teachers who paste two summary means into this box are answering a different question than the principal asked.

Grouped frequency tables (score 10–20: 4 students, 20–30: 7 students) need midpoints and frequencies. The mode of grouped data is often quoted as the modal class - the tallest bar - not a single number. This calculator only sees a raw list. If you type the midpoints 15, 15, 15, 15, 25, 25, … you can manufacture a mode at a midpoint, which is an approximation, not the definition used on raw microdata.

Stem-and-leaf plots and ordered dot plots are just the sorted list with a drawing. The median is still the middle leaf. A common worksheet asks students to build the plot first, then read mean/median/mode; you can check the arithmetic here after the plot is drawn. Do not skip the sort: the median of 4, 8, 6, 5, 3, 8 is not 6 (the unsorted “middle”).

Public dashboards: median household income, median home price, median time-to-hire. Those series stay comparable when a billionaire moves into town. Scientific replicates: mean of three absorbance readings, because the error model is roughly symmetric and you will later quote a standard deviation. Retail: mode of shoe size sold this week, because you restock the size people actually buy, not the arithmetic mean of 8.37.

Likert items (1–5 agree/disagree) are ordinal. Reporting a mean 3.7 is common and controversial; a median of 4 and a mode of 5 may describe the pile-up better. This tool will happily average 1–5 if you paste them. Whether that mean is meaningful is a measurement debate, not a calculator feature.

Time averages versus ensemble averages: the mean of twelve monthly returns is not the same as the compounded annual return. Geometric means and log-returns are finance tools, not this four-pack. Likewise a “trimmed mean” that drops the top and bottom 10% is a robust cousin of the mean; compute it by deleting those order statistics from the paste if a methods section requires it.

Population versus sample wording on a mean is almost cosmetic: both use sum/n. The n versus n−1 split appears only for variance, which is why this page refuses to print an SD. If a rubric says “find the average and the spread,” they may want range (here) or IQR/SD (statistics / SD calculators). Read the rubric; the four-pack is not a mind reader.

Write the six numbers. Add: 4+8=12, +6=18, +5=23, +3=26, +8=34. Divide 34 by 6. 6×5 = 30, remainder 4, so 5 and 4/6 = 5 and 2/3 ≈ 5.666… which rounds to 5.667 at three decimal places. Sort: 3, 4, 5, 6, 8, 8. Two middle values 5 and 6 average to 5.5. Tally frequencies: 8 appears twice, everything else once, so mode 8. Largest 8 minus smallest 3 is range 5. Count 6 and sum 34 sit under the four-pack as a checksum: if your mean times n is not the sum, the mean is wrong.

Change the second 8 to 7: list 4, 8, 6, 5, 3, 7. Now every value is unique, so the mode line becomes no unique mode. Mean becomes 33/6 = 5.5, coincidentally equal to the new median (5 and 6 still the center pair). Range becomes 8−3=5 still. That is a useful reminder that range and median can stay put while mode disappears.

Duplicate the 4 as well: 4, 8, 6, 5, 3, 8, 4. Now 4 and 8 both appear twice. The mode line lists 4, 8 (bimodal). n becomes 7, so the median is the 4th of the ordered 3, 4, 4, 5, 6, 8, 8 which is 5. Mean is 38/7 ≈ 5.429. Range remains 5. Copy those four headlines into a worksheet without re-deriving them from a graph that was drawn from a different list.

If a worksheet wants the mean to three decimals, 5.667 is the rounded value of 5.6̅. Writing 5.66 or 5.67 depends on the rounding rule; this display uses three decimals when the value is that close to a three-decimal number. Always show the sum and n so a grader can reconstruct 34/6.