📊 Mean, Median, Mode & Range Calculator
Enter any list of numbers to get the mean, median, mode and range — including honest multimodal and no-mode results competitors force into one answer.
Sorted values & frequency
| Value | Times it appears |
|---|---|
| 12 | 2 |
| 13 | 2 |
| 14 (mode) | 3 |
| 16 | 1 |
| 19 | 1 |
With an odd count of 9 values, the median is the single middle sorted value.
What Mean, Median, Mode & Range Calculator Does
Mean, median and mode all answer the same underlying question — "what is a typical value in this data?" — but they answer it in three different, sometimes contradictory, ways. The mean is the arithmetic average: add everything up and divide by how many values there are. The median is whatever sits in the exact middle once the values are sorted. The mode is whichever value occurs most often. On a dataset without repeats or skew the three can coincide; on real data they usually do not, and the gap between them is itself informative.
The subtlety a naive implementation gets wrong is the mode, specifically what to do when nothing repeats or when several values tie for most frequent. A dataset like 1, 2, 3, 4 has no value that occurs more often than any other — every value appears exactly once — so the statistically correct answer is "no mode." A weaker tool that always returns a value (often the first or the smallest) is not more helpful, it is wrong. The opposite failure is just as common: real data is frequently multimodal, with two or more values genuinely tied for most frequent, and a calculator that reports only one of them is throwing away real information about the shape of the data.
The median also has a rule that is easy to get backwards: for an odd count of values it is the single middle value once sorted, but for an even count there is no single middle value, so it is the average of the two values that straddle the middle. Skipping the sort step entirely — taking the "middle" of the data in its original entry order — is a common bug in hand-rolled scripts and gives a meaningless answer.
This tool covers central tendency and spread-of-range only. For how spread out the data is around its mean — variance, standard deviation, and whether that spread is large or small relative to the scale of the data — see the standard deviation calculator, which owns that explanation in full rather than repeating it here.
How to Use Mean, Median, Mode & Range Calculator
- Paste or type your numbers, separated by commas, spaces or line breaks
- Read the mean, median, mode and range from the results
- Check the sorted value/frequency table to see exactly which value(s) set the mode
- Watch for the "no mode" or "multimodal" label — both are correct statistical outcomes, not calculator errors
Formula Used by Mean, Median, Mode & Range Calculator
Mean (arithmetic average)
x̄ = (Σxᵢ) ÷ n
- xᵢ
- Each individual value in the data
- Σxᵢ
- The sum of every value
- n
- How many values there are
Worked example
The dataset 2, 4, 4, 4, 5, 5, 7, 9 (n = 8)
- Sum = 2 + 4 + 4 + 4 + 5 + 5 + 7 + 9 = 40
- 40 ÷ 8
Result: x̄ = 5
Median (middle value once sorted)
n odd → the middle value; n even → average of the two middle values
Worked example
The same dataset, sorted: 2, 4, 4, 4, 5, 5, 7, 9 (n = 8, even)
- The two middle values (4th and 5th) are 4 and 5
- Average them: (4 + 5) ÷ 2
Result: median = 4.5
Mode (most frequent value, or values)
mode = the value(s) whose frequency equals the highest frequency in the data
Worked example
The exact dataset behind the common search "what is the mean, median, and mode of 13 16 12 14 19 12 14 13 14"
- Sum = 13+16+12+14+19+12+14+13+14 = 127, and 127 ÷ 9 = 14.1111 → mean
- Sorted: 12, 12, 13, 13, 14, 14, 14, 16, 19 (n = 9, odd) → the 5th value, 14, is the median
- Frequencies: 12 appears twice, 13 appears twice, 14 appears three times, 16 and 19 appear once each
- 14 has the highest frequency (3), so it is the mode; range = 19 − 12
Result: mean = 14.1111, median = 14, mode = 14, range = 7
How to Read Your Result
"No mode" is a real, correct result
When every distinct value in a dataset occurs exactly once, no value is more common than the others, so there is nothing that qualifies as "most frequent." The mathematically honest answer is that the dataset has no mode. Forcing an answer anyway — as some simpler calculators do, typically returning the first or smallest value entered — invents a fact about the data that is not there.
Multimodal data is not a tie you break
If two or more values are tied for the highest frequency, the dataset genuinely has more than one mode: bimodal for two, multimodal for more. Picking just one of the tied values throws away real structure — a dataset that clusters around two different common values (say, two popular price points) is a different shape from one with a single dominant value, and reporting only one mode hides that.
Mean vs. median tells you about skew
When the mean and median are close, the data is roughly symmetric. When the mean sits noticeably higher than the median, a handful of unusually large values are pulling the average up (the classic case is household income or home prices); when the mean sits lower than the median, unusually small values are pulling it down. The median is more resistant to those extreme values because it only depends on which value is in the middle, not on how far away the other values sit.
Limitations & Accuracy Notes
- This calculator treats every entered value as a plain number. For data that already arrives as a grouped frequency table (class intervals with counts), the mean, median and mode are estimated from the class midpoints instead, which is a different calculation not covered here.
- The mode is only meaningful for data with genuine repeated values. For continuous measurements where every value is likely to be unique (e.g. precise sensor readings), "no mode" is the expected and correct result rather than a limitation of the tool.
- Mean and range are both sensitive to a single extreme value; one outlier can move the mean and range substantially while leaving the median almost unchanged. Compare the two before assuming the mean represents a "typical" value.
Frequently Asked Questions
What is the mean, median, and mode of 13, 16, 12, 14, 19, 12, 14, 13, 14?
What is the mean, median and mode of 2, 4, 4, 4, 5, 5, 7, 9?
What if every number in my data appears the same number of times?
Can a dataset have more than one mode?
Why is my median different from my mean?
References & Further Reading
- NIST/SEMATECH e-Handbook of Statistical Methods — Measures of Location: Mean, Median, and Mode — US National Institute of Standards and Technology reference defining mean, median and mode and when each is the more appropriate summary