Average Calculator - Mean, Median, Mode, and Range

An average calculator turns a pile of numbers into a few summary values you can report, compare, or put in a gradebook. In everyday speech “the average” almost always means the arithmetic mean: add every value and divide by how many there are. Statisticians are pickier. They also talk about the median (the middle of the sorted list), the mode (the most common value or values), and the range (the distance from the smallest observation to the largest). Those four ideas answer different questions. The mean is a balance point. The median is a typical middle that ignores how wild the tails are. The mode is what repeats. The range is a crude measure of spread, not a typical score at all.

This free online average tool is built for that full summary, not only a single quotient. Paste a list such as 12, 15, 15, 20 and you immediately get count, sum, mean, median, mode, range, min, and max. Switch to weighted mode when some observations should count more than others - exam weights, credit hours, survey sampling weights, or a lab that averages replicate runs with different reliabilities. Weighted mode reports the weighted mean and the number of pairs as the primary result, because mixing a weighted mean with an unweighted median without saying so is how grade disputes start.

Nothing is uploaded. Parsing and arithmetic run in your browser with JavaScript. After the first load, a dropped connection does not stop the summary. The last list, weighted pairs, and mode setting are stored locally for up to 30 days so a refresh does not erase a gradebook you were checking.

Using this mean, median, mode, and range calculator is straightforward:

1. Choose List for an unweighted summary or Weighted mean for value–weight pairs.
2. For a list, type or paste numbers separated by commas, spaces, or new lines. Mixed separators are fine. Blank tokens are ignored. A completely empty box is rejected.
3. For weighted input, put one pair per line: value, weight. Example: 80, 0.4 on the first line and 90, 0.6 on the second. Weights must be non-negative. A total weight of zero is rejected.
4. Read the right-hand panel. Copy the summary, or clear the box to start over. The last input is saved locally in your browser.

Note: letters, stray punctuation, and blank fields that are not empty tokens are rejected. Scientific notation such as 1e3 is accepted when the token is a complete number.

Take the default list on this page: 12, 15, 15, 20. The count n is 4. The sum is 12 + 15 + 15 + 20 = 62. The arithmetic mean is 62 / 4 = 15.5. That is the unique number that, if every observation equalled it, would produce the same total. It is also the number a basic calculator would give you if you added the four scores and divided by four - sequential addition, then one division.

The mean uses every observation, which is a feature and a trap. One extreme value pulls it. A class of exam scores 72, 75, 78, 80, 82 has mean 77.4. Replace the last 82 with a 20 from a missed exam that was scored as zero-plus-something, and the mean drops several points even though four of the five students barely moved. That is why a report that only quotes “the average” can describe a room that nobody in the room actually occupies. Pair the mean with the median and the range, which this calculator prints together so you can see the pull.

Count and sum are shown on purpose. If you are checking a spreadsheet, you should be able to confirm that n matches how many cells you thought you selected and that the sum matchesSUM() before you trust the division. Off-by-one errors - a blank cell counted as zero, a header row included, a student counted twice - are more common than arithmetic mistakes.

To find the median, sort the list from smallest to largest. If n is odd, the median is the single middle value, at position (n + 1) / 2 in the sorted list. If n is even, there is no single middle observation, so the median is the arithmetic mean of the two central values - the entries at n/2 and n/2 + 1.

For 12, 15, 15, 20 the sorted list is already in order. n = 4 is even, so the two central values are the second and third numbers: 15 and 15. Their average is 15. The mean was 15.5; the median is 15. They are close here because the list is short and fairly tight. On a skewed income list or a reaction-time list with a few very large outliers, the median often sits where a “typical” person actually is, while the mean sits somewhere in the tail.

The median does not use the numeric distance of the extremes, only their order. Raising the 20 to 200 leaves the median of this four-point list unchanged at 15, while the mean jumps. That robustness is why housing reports quote median sale price, and why some teachers look at a median test score before they rewrite a curve. It is not always “better” than the mean. It answers a different question: what is the middle of the ordered sample, not what total would you split equally.

The mode is the value that appears most often. In 12, 15, 15, 20 the value 15 appears twice and everything else once, so the mode is 15. If two different values share the highest frequency, the list is multimodal and this calculator lists every mode rather than pretending there is a single winner. If every value appears once, there is no unique mode - all frequencies are equal - and the tool says so instead of dumping the entire list as “the mode.”

Mode is the natural summary for categorical data (favorite color, blood type, most common error code) and for discrete scores with genuine repeats (quiz marks out of 10). It is a weak summary for continuous measurements that almost never repeat exactly. Ten reaction times to six decimal places will usually have no unique mode even though the distribution has a clear peak if you bin the data. Do not force a mode onto data that were never going to tie.

Ties at the top are not a bug. A bimodal homework-score histogram - a cluster who finished the worksheet and a cluster who left it blank - is educationally important. Reporting both modes is more honest than averaging them into a number that describes neither group. This page follows that rule: every value with the maximum frequency is listed.

Range is maximum minus minimum. For 12, 15, 15, 20 the min is 12, the max is 20, and the range is 8. Range is easy to explain and easy to abuse. It uses only two points, so a single typo (a 2 that became 200) inflates it. It also depends on sample size: larger samples tend to produce more extreme minima and maxima even when the underlying spread has not changed, which is why researchers prefer standard deviation or interquartile range for formal work.

Still, range is the right first check for “did I paste the wrong column?” If you expected exam scores out of 100 and the max is 1000, you pasted percents-as-counts or an extra zero. Min and max are printed beside the range so you can see which end moved. Range is a spread measure, not an average; calling it “the average spread” in a caption is misleading. This calculator keeps it in the same panel as mean and median so you remember it is part of the summary, not a rival mean.

A weighted average (weighted mean) is used when observations should not all count the same. The formula is:

Suppose Maya’s course syllabus publishes the following category weights. These are the numbers you would type in weighted mode, one pair per line:

The unweighted mean of the five category scores is (95 + 88 + 72 + 64 + 91) / 5 = 410 / 5 = 82. That number pretends homework, a thin quiz average, a project, a weak midterm, and a strong final are equally important. The syllabus says they are not.

The weighted products sum to 19.00 + 8.80 + 14.40 + 16.00 + 22.75 = 80.95. The weights already add to 1.00, so the weighted mean is 80.95 / 1.00 = 80.95. Maya’s course average is a little lower than the naive 82 because the midterm 64 carries a quarter of the grade and the sparkling homework 95 only carries a fifth. If she wants the course mean to match the unweighted 82, she cannot “make it up” with more homework points; she has to move a heavily weighted exam.

You can type the same pairs as percents (20, 10, 20, 25, 25) instead of decimals (0.20, 0.10, …) as long as you are consistent. Σ(value × weight) / Σ(weight) is unchanged if every weight is scaled by the same positive constant. What you must not do is mix 0.20 on one line with 25 on another and assume they still mean “twenty percent.” This calculator will happily compute that inconsistent mix; it cannot read a syllabus. Check that the sum of weights is 1 (proportions), 100 (percent points), or the total credit hours you intended.

Negative weights are rejected because they do not mean “this category counts less” in a gradebook; they invert the contribution and can manufacture a mean that lies outside the scores. A zero total weight is rejected because division by zero is not an average. Individual zeros are allowed: a category with weight 0 is simply omitted from the weighted mean, which is the same as deleting that line.

Credit-hour GPA is the same pattern: each course grade is a value, each credit hour is a weight. A 4-credit major course should move the GPA more than a 1-credit lab. Treating every course as weight 1 is the unweighted mean of course marks, not a GPA. Paste the pairs here, confirm Σ weights equals total credits, and copy the weighted mean into the report.

Quote the mean when every observation should count equally and you care about the total (average daily sales, mean replicate concentration, mean time per task). Quote the median when the question is “what is typical?” and a few extremes should not dominate (home prices, wait times, most human-size measurements with a long tail). Quote the mode when the question is “what happens most often?” (most common defect code, most frequent quiz score). Quote a weighted mean when a policy document already assigned importance: syllabus percents, credits, survey weights, or combining class means of different sizes (the combined mean of two sections is not the mean of the two section means unless the sections have equal n).

Combining section means is a classic mistake. Section A has 10 students with mean 90. Section B has 40 students with mean 70. The mean of 90 and 70 is 80, but the combined class mean is (10 × 90 + 40 × 70) / 50 = 74. That is a weighted mean with weights equal to the section sizes. If you only have the two means and the two counts, weighted mode on this page is the right tool: 90, 10 and 70, 40.

Outliers deserve a sentence in the write-up, not a silent deletion. If you drop a value, say so and recompute. If you keep it, the mean will show it and the median may not - which is information, not a contradiction. Range will scream. Use all four list statistics before you decide the story.

For inference - “is this mean different from a hypothesized value?” - you need a p-value and a model, not only a descriptive average. After you have the sample mean, the p-value calculator is the next tool, not a substitute for looking at median and range first.

The list parser splits on commas, whitespace, and semicolons, then throws away empty pieces. That lets you paste a column from Excel, a row of CSV, or a sentence like “12 15, 15; 20” and still get four numbers. What it will not do is guess that “fifteen” means 15, or that a currency symbol is decoration. A token with letters, two dots, or a leftover unit like 15pts is rejected with a message that quotes the bad token so you can delete it.

Thousands separators are a regional trap. 1,234 in US grouping is one thousand two hundred thirty-four; in this parser a comma is a splitter, so you get 1 and 234. Strip grouping commas before you paste, or use a space-separated column of plain decimals. Leading plus signs and ordinary scientific notation (1e3, -2.5E-1) are accepted. A bare decimal point is not a number.

Weighted lines are stricter: exactly two numeric tokens per non-empty line. A comment, a third column, or a header row named “score, weight” will fail until you remove it. That strictness is deliberate. Silently ignoring a third column is how a copied “notes” field becomes a phantom weight.