MEAN MEDIAN MODE CALCULATOR
Find the mean, median and mode of any list of numbers, and learn how each one works in simple words.
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Choose a calculator. They all use the same engine, so the working and the methods match everywhere.
Mean, median and mode are three ways to describe a list of numbers. This website helps you find all three and shows how each answer is worked out.
Type or paste your numbers into the calculator, press Calculate, and read the result with its steps. You can also find the range, minimum and maximum.
You do not need to be good at maths to start. Each section below explains one idea with a small example.
What Is Mean, Median and Mode?
The mean, median and mode are measures of central tendency. This long name has a simple meaning: each one tells you what is typical in a data set, which is just a list of numbers.
Mean
The mean is the average most people learn first. Add up all the numbers, then divide by how many numbers there are.
Mean = sum of the values ÷ number of values
Example
Numbers:
4, 6, 8
4 + 6 + 8 = 18
18 ÷ 3 = 6
The mean is 6.
Median
The median is the middle value after you put the numbers in order from smallest to largest.
Example
Numbers in order:
3, 5, 7, 9, 11
The middle number is 7, so the median is 7.
When there is an even number of values, there are two middle numbers. Add them and divide by 2. For 2, 4, 6, 8, the median is (4 + 6) ÷ 2 = 5.
Mode
The mode is the value that appears most often.
Example
Numbers:
2, 4, 4, 5, 7
The number 4 appears twice and the others appear once, so the mode is 4.
A data set can have one mode, more than one mode, or no mode. The list 1, 2, 3 has no mode because every value appears once.
One Calculator, Several Ways to Enter Data
The site has one main statistics calculator. You choose how your data is written, and the same tool does the work.
- A simple list of numbers
- Values with their frequencies
- Grouped class intervals
- Weighted values
- Mean, median and mode
- Range, minimum and maximum
- Quartiles and interquartile range
- Population and sample variance and standard deviation
- Percentiles
- Frequency distributions
- Five-number summary
- Practice and learning resources
For advanced results, such as grouped-data estimates and percentiles, the calculator explains the method it used. You can then compare it with the method in your own course.
How to Find the Mean, Median and Mode by Hand
A good calculator shows the working, not only the answer. Here is the same working you can do on paper.
Example
Data set:
3, 7, 7, 2, 9
Step 1. Sort the numbers:
2, 3, 7, 7, 9
Step 2. Mean. The sum is 28 and there are 5 values, so 28 ÷ 5 = 5.6.
Step 3. Median. The middle of five numbers is the third one, so the median is 7.
Step 4. Mode. The number 7 appears twice, so the mode is 7.
Use this to check homework or to see where a mistake crept in.
Learn Statistics in Simple Words
This website also explains the ideas behind the calculator in plain language.
You can learn about:
- Data sets
- Averages
- Mean, median and mode
- Frequency and frequency tables
- Grouped data
- Weighted values
- Range
- Variance and standard deviation
- Quartiles and percentiles
- Outliers
Every idea comes with a small example, so you can connect the formula to real numbers.
Who Can Use This Website?
Anyone who works with a list of numbers can use it.
Students
Check your homework answers and see how each result was found.
Teachers
Make quick examples, check calculations and explain statistics in class.
Parents
Help your child with homework by looking at the steps together.
Researchers and Data Users
Check simple calculations before moving on to more advanced analysis.
Anyone Learning Statistics
You do not need to be at school or university. Learn at your own speed.
What Is the Difference Between Mean and Median?
Both are kinds of average, but they can give different answers. In everyday talk, "average" usually means the mean. The median and the mode are averages too.
Example
Numbers:
2, 3, 4, 5, 36
Mean = (2 + 3 + 4 + 5 + 36) ÷ 5 = 50 ÷ 5 = 10
Median = 4
One very large number, 36, pulls the mean up but hardly moves the median. When a few values are far bigger or smaller than the rest, the median often shows a more typical value. When the values are fairly even, the mean is useful because it uses every number.
How are mean, median and mode related?
If the data is balanced on both sides and has one mode, the three values are equal or very close. If the data is lopsided, they move apart. For moderately lopsided data, some textbooks use a rough estimate: Mode ≈ 3 × Median − 2 × Mean. It is only an estimate, not an exact answer.
More Than Mean, Median and Mode
Three numbers do not always tell the whole story. You may also want to know how spread out the values are.
The range is the largest value minus the smallest value.
Example
3, 5, 7, 9, 11
Range = 11 − 3 = 8
Quartiles split ordered data into four parts. The interquartile range, or IQR, shows the spread of the middle half of the data. Variance and standard deviation also measure spread.
Helpful for Real-World Data
Statistics is not only a school subject.
A shop can look at daily sales. A teacher can look at test scores. A scientist can look at measurements. A sports fan can look at player numbers.
Simple measures turn a long list of numbers into something easier to understand.
Free and Easy to Use
You can use the calculators without installing any software.
The website works on computers, laptops, tablets and phones.
Enter your data, press Calculate and read the result.
Start With Your Numbers
Statistics is easier when you take it one step at a time.
Enter your data, choose the calculator that fits your problem, and read the result with its steps. Then use the learning sections to see why the answer works.
At Mean Median Mode Tool, our goal is simple: make statistics easier to calculate and easier to understand.
Work out your mean, median and mode now
Enter your numbers, press Calculate and read the working. Free, no sign-up, and your data never leaves your browser.