Mode Calculator
This page opens the average calculator with the mode as its headline figure instead of the mean: the mode is the value that turns up most often in a list. On a first visit the box arrives filled with twelve numbers, 18, 22, 31, 39, 44, 46, 51, 58, 62, 70, 76 and 83, and every one of them is different, so the first answer reads None and explains itself: all 12 values appear exactly once, so nothing is more common than anything else. Paste your own numbers over the sample and the big figure becomes the value that repeats most, with the count printed under it. For 2, 4, 4, 4, 5, 5, 7, 9 that line reads 4 appears 3 times: more often than any other value. When several values tie, every one of them is reported rather than the first or the smallest, and the mean, median, range, both standard deviations, both variances, the geometric and harmonic means and the sum stay listed underneath, each with its arithmetic written out.
Commas, spaces, tabs, semicolons and new lines all separate values, so a column pasted straight out of a spreadsheet works. Currency symbols, percent signs and accounting parentheses are understood; anything left over is listed rather than silently dropped.
(18 + 22 + 31 + … + 83) ÷ 12 = 600 ÷ 12 = 50 The arithmetic mean: the one most people mean by “average”.
Sorted: 18, 22, 31, …, 83, an even count (12), so the median is the average of the 6th and 7th values: (46 + 51) ÷ 2 = 48.5
All 12 values appear exactly once, so nothing is more common than anything else: there is no mode. No mode is a real answer, not a failure. Adding a repeat would create one.
Largest − smallest = 83 − 18 = 65
√(sample variance) = √428.72727272727275 = 20.705730432111608 Divides by n − 1. Use this when your numbers are a sample drawn from something larger.
Σ(x − mean)² ÷ (n − 1) = 4716 ÷ 11 = 428.72727272727275 Divides by n − 1. Use this when your numbers are a sample drawn from something larger.
√(population variance) = √393 = 19.82422760159901 Divides by n. Use this when your numbers ARE the whole group.
Σ(x − mean)² ÷ n = 4716 ÷ 12 = 393 Divides by n. Use this when your numbers ARE the whole group.
(18 × 22 × 31 × … × 83)^(1/12) = 45.487558964974305 The geometric mean: the right average for growth rates, ratios and anything that multiplies.
12 ÷ (1/18 + 1/22 + … + 1/83) = 12 ÷ 0.29584565082861597 = 40.56169143061571 The harmonic mean: the right average for speeds, rates and other per-unit quantities.
18 + 22 + 31 + … + 83 = 600
Common questions
- How do you find the mode of a set of numbers?
- Count how many times each value appears and take the value with the highest count. For 2, 4, 4, 4, 5, 5, 7, 9 there is one 2, three 4s, two 5s, one 7 and one 9, so the mode is 4, and the line under the big figure reads: 4 appears 3 times, more often than any other value. You do not have to sort or group anything first. The page counts a copy of your values and prints the count it found beside the answer, so the result can be checked rather than taken on trust.
- What if two or more values appear the same number of times?
- All of them are modes and all of them are reported. Paste 1, 2, 2, 3, 3, 4 and the answer reads 2, 3 above the line: 2 values tie for most common, 2 and 3, each appearing 2 times, so this data is multi-modal. Returning only the first value, the smallest, or a zero is the usual failure here, and it is wrong in a way you cannot see from the answer. When more than eight values tie, the first eight are shown followed by how many more there are, and when every distinct value ties a note says the mode is not picking anything out: paste 1, 1, 2, 2, 3, 3 and all three are modes at two appearances each.
- What does it mean when there is no mode?
- It means every value in the list appears exactly once, so nothing is more common than anything else. The twelve numbers this page opens with are that case, which is why the first answer reads None rather than a figure, with the reason under it and the reminder that no mode is a real answer, not a failure: adding one repeat would create a mode. A list of a single number is the same case, worded for one value. The answer is never 0 and never the first or the smallest value, because either would read as a finding about your data when it is only a made-up choice.
- Mode, mean or median: which one do I want?
- The mode when you want the value that comes up most: the size ordered most often, the score most pupils got, the delivery time that recurs. The mean when the quantities genuinely add up. The median when a few outliers would drag the mean somewhere unrepresentative. You do not have to choose here, because the mode is the big figure on this page while the mean, median, range, both standard deviations, both variances, the geometric and harmonic means and the sum are listed underneath at the same time. The Featured result menu holds those nine, and switching it moves another one to the top. This page always opens on the mode, even if you last chose a different statistic or last used the weighted mean, because the page you asked for wins. Your last list of numbers does come back, so you can carry on where you left off.
- Do 4, 4.0 and 4.00 count as the same value?
- Yes. Values are compared as numbers, not as the text you typed, so 4, 4, 4.0 and 4.00 is one value appearing 4 times, and the note adds that every value here is the same, so it is the mode by default. 0 and a negative zero are one value for the same reason. Currency symbols, percent signs and accounting parentheses for negatives are read off before anything is counted, so two entries of $1,200 beside one $980 give a mode of 1200, with a note saying the comma in $1,200 was read as grouping thousands and how to write it if you meant two separate numbers.
- Can it find the mode of words, letters or categories?
- No, this box reads numbers. Anything that is not a number is skipped and named above the results rather than quietly counted as zero, so 10, 20, n/a, 30 reports that it skipped one entry, quotes it, and works from the other three. If nothing in the box is a number at all, the message names the words it could not read and shows how to separate values. For categories, number them first, small 1, medium 2, large 3, and the mode of those numbers is the most common category. Commas, spaces, tabs, semicolons, pipes and new lines all separate values, so a column copied straight out of a spreadsheet goes in as it is.
Exact for median, mode, minimum, maximum and range. The mean, variances and standard deviations use compensated summation and are accurate to roughly 15 significant digits, not claimed as exact, because double-precision arithmetic is not.