Mean, Median, Mode Calculator
Enter a list of numbers — separated by commas, spaces or new lines — and get the mean, median and mode, along with the count, sum, minimum and maximum.
Calculator
- Comma, space or newline input
- Sorted median
- Multimodal support
- Count, sum, min, max
Result & calculation receipt
- Method
- Sum ÷ count for the mean; middle of the sorted list for the median; most frequent value(s) for the mode
- Formula
mean = Σx / n; median = middle of sorted data; mode = most frequent value- Substitution
- mean = 108 / 6 = 18
- Steps
- Sorted: [4, 8, 15, 16, 23, 42].
- Sum = 108, count n = 6, mean = 18.
- Median = average of the two middle values = (15 + 16)/2 = 15.5.
- Mode: no mode (every value appears once).
- Verification
- Sum of deviations from the mean = 0 ≈ 0, confirming the mean.
- Decimal result
- mean: 18 · median: 15.5 · min: 4 · max: 42 · sum: 108 · count: 6
- Engine
- math-solvers v1.4.0
How this calculator works
The calculator parses the data, sums it and divides by the count for the mean, sorts it to find the median (the middle value, or the average of the two middle values for an even count), and tallies frequencies to find the mode (the most common value, or values, or none if all are unique). It cross-checks the mean by confirming the deviations from it sum to zero.
Worked example
For 4, 8, 15, 16, 23, 42 the mean is 108 ÷ 6 = 18, and the median is the average of the two middle sorted values (15 and 16), or 15.5. For 2, 5, 5, 7, 9 the mode is 5, because it appears twice. Data with two equally-common values is reported as multimodal.
Key insight
The three averages answer different questions: the mean is the balance point, the median is the middle value that resists outliers, and the mode is the most typical value. When a data set is skewed, the mean and median can diverge sharply — which is exactly what makes comparing them informative.
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the sum divided by the count (the average). The median is the middle value when the data is sorted. The mode is the value that appears most often. They can all differ, especially in skewed data.
How is the median found for an even number of values?
Sort the data and average the two middle values. For six values, the median is the mean of the third and fourth. The calculator shows the sorted list it used.
Can a data set have more than one mode?
Yes. If two or more values tie for the highest frequency, the set is multimodal and the calculator lists all of them. If every value is unique, there is no mode.
How do I enter my data?
Separate the numbers with commas, spaces or new lines — mix them freely. Non-numeric entries return an error identifying the offending value.
Why does the calculator show min, max, count and sum?
They describe the range and size of the data and are the building blocks of the averages, so seeing them makes the result easier to sanity-check.
Methodology & verification
The data set is parsed from comma-, space- or newline-separated numbers. The mean is the sum divided by the count; the median is the middle of the sorted data (or the mean of the two central values); the mode is the most frequent value or values, with unique data reported as having no mode. Empty input and non-numeric values return structured errors. The mean is verified by confirming the deviations from it sum to (approximately) zero, and count, sum, minimum and maximum are reported.
Engine: math-solvers v1.4.0 · Last reviewed: · Every result is computed client-side and never sent to a server. See the verification methodology and the scientific calculator validation.