Mean, Median, Mode Calculator
Enter a list of numbers to calculate the mean (average), median, mode, and range — with every step shown so you can follow the working.
- 01Find the mean (average), median, and mode of any data set instantly.
- 02Also get range, minimum, maximum, midrange, count, and sum.
- 03See step-by-step working so you can learn and check homework.
- 04Paste numbers separated by commas, spaces, or new lines.
- 05100% free and private — every calculation runs in your browser.
Mean, Median, Mode Calculator
Try an example data set
Mean (Average)
15
Median
14
Mode
13
Appears 4 times
Count (n)
9
Sum (Σx)
135
Range
8
Minimum
13
Maximum
21
Midrange
17
Step-by-step calculation
- 01Mean = Σx ÷ n = 135 ÷ 9 = 15
- 02Sort the values: 13, 13, 13, 13, 14, 14, 16, 18, 21
- 03Median = middle value of the sorted list = 14
- 04Mode = most frequent value(s) = 13 (appears 4 times)
Why Use This Mean, Median, Mode Calculator
All Three Averages at Once
Get the mean, median, and mode together so you can compare the three measures of central tendency for the same data set — useful when one average alone could be misleading.
Step-by-Step Working
See exactly how each result is found: the sum divided by the count for the mean, the sorted list and middle value for the median, and the frequency count for the mode. Perfect for homework and exam revision.
More Than Averages
Alongside the mean, median, and mode, the calculator reports the range, minimum, maximum, midrange, count, and sum — a quick descriptive summary of your data.
Handles Multimodal Data
If two or more values are tied for the highest frequency, the calculator lists every mode. If all values are unique, it correctly reports that the data set has no mode.
Flexible Data Input
Paste numbers separated by commas, spaces, tabs, or new lines. Decimals and negative numbers are supported, so you can drop in a column straight from a spreadsheet.
Free, Instant, and Private
Everything runs in your browser with no server round-trips, no signup, and no limits. Your data never leaves your device and results appear instantly.
Mean, Median, and Mode Explained
The mean, median, and mode are the three most common measures of central tendency — they each describe the 'centre' or typical value of a data set in a different way. Looking at all three gives a fuller picture of your data than any single average.
Whether you are a student, teacher, or analyst, this mean median mode calculator gives instant, step-by-step central-tendency results for any data set.
- Mean (Average)
- The mean is the sum of all values divided by how many there are. It uses every value, which makes it powerful but also sensitive to outliers — a single very large or very small number can pull the mean away from the typical value.
- Median
- The median is the middle value when the data is sorted in order. If there is an even number of values, it is the average of the two middle ones. The median is resistant to outliers, so it often describes skewed data better than the mean.
- Mode
- The mode is the value that appears most often. A data set can have one mode, several modes (multimodal), or no mode at all if every value is unique. The mode is the only average that also works for non-numeric categories.
- Which Average Should You Use?
- Use the mean for roughly symmetric data, the median for skewed data or data with outliers, and the mode when you care about the most common value. Comparing all three reveals the shape of your data.
How to Use the Mean, Median, Mode Calculator
- 01
Enter your numbers
Type or paste your data set into the input box. Separate values with commas, spaces, or new lines — for example 13, 18, 13, 14, 16. Decimals and negative numbers are supported.
- 02
Click Calculate
Press the Calculate button. The tool parses your numbers and computes the mean, median, and mode instantly in your browser.
- 03
Read the results
The headline cards show the mean, median, and mode. Below them you get the range, minimum, maximum, midrange, count, and sum for a full summary of your data.
- 04
Review the steps
Open the step-by-step section to see how each value is found — the sum and count for the mean, the sorted list for the median, and the frequency for the mode. Great for learning and checking homework.
Tips for Finding Mean, Median, and Mode
Sort Before Finding the Median
The median is the middle of the sorted data, so always order the values first. With an even count, average the two middle values. This calculator sorts for you and shows the ordered list.
Watch Out for Outliers
The mean is pulled toward extreme values, while the median is not. If your data has outliers, the median often describes the typical value better than the mean.
Remember Mode Can Be None or Many
If every value occurs once, there is no mode. If several values tie for the highest frequency, the data set has multiple modes. Both are valid results.
Compare All Three
When the mean, median, and mode are close, the data is roughly symmetric. When they differ a lot, the data is skewed — comparing them tells you about the distribution's shape.
Keep Units Consistent
Make sure every value is in the same unit before calculating. Mixing units (for example minutes and hours) will produce a meaningless average.
Don't Round Too Early
Keep full precision while calculating and round only the final mean or median for reporting. Rounding intermediate values can introduce small errors.
Mean, Median, Mode Formulas and Definitions
Measures of central tendency
The mean, median, and mode each summarise the typical value of a data set. The best one to use depends on the shape of the data and whether it contains outliers.
When to use each average
- Mean — best for roughly symmetric data with no extreme outliers.
- Median — best for skewed data or data with outliers.
- Mode — best when you care about the most common value or category.
- Compare all three to understand the distribution's shape.
Range and midrange
The range is the difference between the maximum and minimum values, and the midrange is their average. Both give a quick sense of how spread out the data is.
Key Formulas
Mean
Mean = Σx ÷ n
Example: (4 + 8 + 6) ÷ 3 = 6.
Median (odd count)
Median = the middle value of the sorted data
Example: for 3, 5, 9 the median is 5.
Median (even count)
Median = average of the two middle sorted values
Example: for 3, 5, 8, 10 the median is (5 + 8) ÷ 2 = 6.5.
Mode
Mode = the value(s) that appear most often
Example: for 2, 4, 4, 5 the mode is 4.
Range
Range = maximum − minimum
Example: for 4, 9, 15 the range is 15 − 4 = 11.
Midrange
Midrange = (maximum + minimum) ÷ 2
Example: for 4, 9, 15 the midrange is (15 + 4) ÷ 2 = 9.5.
Mean, Median, Mode Calculator FAQ
Q01How do I find the mean, median, and mode?
The mean is the sum of all values divided by the count. The median is the middle value when the numbers are sorted (or the average of the two middle values for an even count). The mode is the value that appears most often. This calculator finds all three and shows the working.
Q02What is the difference between mean, median, and mode?
The mean is the arithmetic average and uses every value. The median is the middle of the sorted data and is resistant to outliers. The mode is the most frequent value. Together they describe the centre of a data set in three complementary ways.
Q03How do I calculate the average?
The average, or arithmetic mean, is the sum of all the numbers divided by how many numbers there are. For example, the average of 4, 8, and 6 is (4 + 8 + 6) ÷ 3 = 6. Enter your numbers above and the calculator does it instantly.
Q04Can a data set have more than one mode?
Yes. If two or more values are tied for the highest frequency, the data set is multimodal and has several modes. This calculator lists every value that shares the highest frequency.
Q05What if there is no mode?
If every value appears the same number of times (for example, each value occurs exactly once), the data set has no mode. The calculator reports this rather than picking a value arbitrarily.
Q06How do I find the median of an even number of values?
Sort the values and take the average of the two middle numbers. For example, for 3, 5, 8, 10 the two middle values are 5 and 8, so the median is (5 + 8) ÷ 2 = 6.5.
Q07Is my data sent to a server?
No. The calculator runs entirely in your browser using JavaScript. Your numbers are never uploaded or stored, so it is safe for private or sensitive data.
Q08Is this calculator free?
Yes, it is completely free with no limits, no signup, and no premium tier. Calculate the mean, median, and mode for as many data sets as you like.