Mean, Median, Mode & Range
Enter any set of numbers — get the mean, median, mode and range with full step-by-step working.
Mean, median, mode & range
Step-by-step solution
Enter a list of numbers and press Calculate
Mean, Median, Mode & Range Explained
Core concepts, classroom applications, and plain-English explanations for all audiences.
Before the maths — why this matters
You see a headline: "Average salary in the UK is £35,000." But are you above or below average? It depends whether that's the mean or the median — and it makes a huge difference. A single banker earning £1,000,000 in a group of 10 teachers earning £35,000 each pulls the mean up to £150,500. The median is still £35,000. Same data, very different story.
Worked example
"A football team scores these goals in 7 matches: 1, 3, 2, 5, 3, 0, 3. Find the mean, median, mode and range."
Sorted: 0, 1, 2, 3, 3, 3, 5
Mean: (0+1+2+3+3+3+5) ÷ 7 = 17 ÷ 7 ≈ 2.43
Median: middle value = 3
Mode: 3 (appears 3 times)
Range: 5 − 0 = 5
Note: mode and median agree here, but they often don't — especially with skewed data.
Choosing the right average
- → Mean: best when data is evenly spread — class test scores, average temperature across a week.
- → Median: best when there are outliers — house prices, salaries, wait times.
- → Mode: best for categories — most popular shoe size, most common response in a survey.
Critical thinking tip
Whenever you see "average" in a headline or advertisement, ask: mean or median? Estate agents tend to use mean house prices (inflated by large properties). Government reports on wages often use median (more representative). The word "average" alone tells you nothing about which one.
Which average should you use?
Mean
Sum ÷ Count
Use when: Most data sets — especially when values are evenly spread
Avoid when: When there are extreme outliers — one very high or low value skews the mean significantly
Median
Middle value when sorted
Use when: Data with outliers or skewed distributions — e.g. house prices, salaries
Avoid when: Not ideal when you need every value to count equally
Mode
Most frequent value
Use when: Categorical data or when the most popular value matters — e.g. shoe sizes, survey responses
Avoid when: Datasets with no repeated values, or where every value appears the same number of times
Understand Your Data with Mean, Median, Mode & Range
The mean, median, mode, and range are fundamental statistical measures that help us understand and summarise a set of data. They provide different insights into the 'average' value and the 'spread' of the numbers.
Our calculator makes it easy to find all four of these measures for any list of numbers you provide. Simply enter your data, and we'll show you the results along with clear, step-by-step working, perfect for KS3 and GCSE students.
How to Use the Mean, Median, Mode & Range Calculator
Enter Your Numbers
Type or paste your list of numbers into the input box. Separate each number with a comma (e.g., 5, 12, 8, 15, 10).
Click 'Calculate'
Once your numbers are entered, click the 'Calculate' button to process your data.
View Your Results
The calculator will instantly display the Mean, Median, Mode, and Range for your dataset.
See Step-by-Step Working
Below the results, you'll find a detailed breakdown of how each measure was calculated, helping you understand the process.
Common mistakes to avoid
- Calculating the median without ordering the numbers first:The median is defined as the middle value, but only when the data is arranged from smallest to largest (or largest to smallest). If you don't sort, you won't find the true middle. Always sort your data in ascending order before finding the median. For example, for 5, 2, 8, 3, 7, you must sort to 2, 3, 5, 7, 8 before identifying 5 as the median.
- Confusing the mode with the highest frequency count:The mode is the value that appears most often, not how many times it appears. For example, if '7' appears 3 times, the mode is 7, not 3. Identify the number itself that has the highest frequency. If '7' appears 3 times and no other number appears more than 3 times, then 7 is the mode.
- Forgetting to divide by the total count when calculating the mean:The mean is the sum of all values divided by the number of values. A common error is to just sum the numbers. Mean = Sum of all values / Total count of values. Always count how many numbers are in your dataset.
- Incorrectly calculating the median for an even number of values:When there's an even number of values, there isn't a single 'middle' number. Students sometimes pick one of the two middle numbers or just guess. For an even number of values, find the two middle numbers (after sorting), add them together, and then divide by 2 to find their average. This average is the median.