Mean, Median & Mode Calculator
Enter up to five numbers to compute the arithmetic mean and range. The calculator also explains how to determine the median (middle value) and mode (most frequent value) manually — two measures of central tendency that require sorting and frequency counting, which are illustrated in detail below.
Advertisement
Calculator
See your Mean, Median & Mode Calculator results
Enter your email to unlock results — free forever.
No spam, ever. Unsubscribe at any time.
Advertisement
Formula
Mean = Σx / n | Range = Max − Min
The mean is the sum of all values divided by the count. The range is the difference between the largest and smallest values — a simple measure of spread. For the median: sort the values in ascending order and pick the middle one (for odd n) or average the two middle ones (for even n). For the mode: count how many times each value appears; the value with the highest frequency is the mode. If no value repeats, there is no mode; if multiple values tie, all are modes.
How to use the Mean, Median & Mode Calculator
- 1
Enter your number 1
- 2
Enter your number 2
- 3
Enter your number 3
- 4
Enter your number 4
- 5
Enter your number 5
- 6
Read your results instantly
Results update in real time as you type.
Advertisement
Finding the median step by step
The median is the middle value of a sorted dataset. For the default values {2, 4, 4, 6, 8}:
Step 1 — Sort in ascending order: 2, 4, 4, 6, 8. Step 2 — Count values: n = 5 (odd). Step 3 — The median is at position (n+1)/2 = 3. The third value is 4.
For an even count, say {2, 4, 4, 6}: n = 4, so average the 2nd and 3rd values: (4 + 4)/2 = 4.
The median is resistant to outliers. In the dataset {1, 2, 3, 4, 100}, the median is 3 while the mean is 22. For household incomes, home prices, and any skewed distribution, the median is the more informative center.
Finding the mode
The mode is the value that appears most frequently. For {2, 4, 4, 6, 8}: 4 appears twice, all others once — so 4 is the mode.
A dataset can be unimodal (one mode), bimodal (two modes), or multimodal. If every value appears the same number of times, there is no mode.
Mode is especially useful for categorical data where mean and median don't apply. In a survey asking "what size shirt do you wear?" the mode tells you the most popular size to stock — mean and median are meaningless for such data.
In continuous numerical data, mode is often defined over bins (intervals) — the bin with the highest frequency is called the modal class.
Advertisement
When to use which measure
The right measure of central tendency depends on your data and question.
Use the mean when data is roughly symmetric and free of extreme outliers. Test scores, heights, and reaction times often work well. The mean uses all information in the dataset.
Use the median when data is skewed or contains outliers — incomes, home prices, wait times. The median is robust: it doesn't care how extreme the largest value is.
Use the mode when you want the most typical category — shoe sizes, survey responses, color preferences. Mode is the only measure appropriate for purely nominal (categorical) data.
Reporting all three gives readers the fullest picture: mean for mathematical completeness, median for typical experience, mode for most common outcome.
Tips & Insights
Bimodal distributions signal two populations
If your data has two modes, it may represent a mixture of two distinct groups — for example, the heights of all adults peak around 5'4" for women and 5'9" for men. A single mean or median obscures this structure. Always visualize data before relying on summary statistics.
The mean equals the median in symmetric distributions
For perfectly symmetric distributions (like the normal/bell curve), mean = median = mode. Asymmetry between mean and median is a direct signal that the distribution is skewed. When mean > median, the data is right-skewed (long right tail); when mean < median, it's left-skewed.
Range is a crude spread measure
Range only uses two data points — the maximum and minimum — ignoring everything in between. A dataset of {1, 50, 50, 50, 100} and {1, 2, 50, 98, 100} both have range 99, but are very different distributions. For a better spread measure, use interquartile range (IQR) or standard deviation.
Worked Examples
Analyzing class test scores
Mean = 79.2. Sorted: 63, 72, 85, 85, 91. Median = 85 (3rd value). Mode = 85 (appears twice). Range = 91 − 63 = 28. The median and mode both suggest 85 as the typical score, while the mean is pulled down by the outlier of 63.
Salary dataset with an outlier
Mean = 79k. Median = 47k. Mode = none. Range = 168k. The mean ($79k) overstates the typical worker's pay by 68%; the median ($47k) is far more representative. The CEO's $210k salary inflates the mean.
Advertisement
Frequently Asked Questions
What is the difference between mean, median, and mode?
Mean is the arithmetic average (sum ÷ count). Median is the middle value when sorted. Mode is the most frequently occurring value. They all describe the center of a dataset but react differently to outliers and skew.
Can a dataset have more than one mode?
Yes. A dataset is bimodal if two values tie for highest frequency, and multimodal if more. If every value appears exactly once, there is no mode.
Why is the median preferred for income data?
Income distributions are heavily right-skewed — a small number of very high earners pull the mean upward. The median is unaffected by how extreme the top earners are, making it a better measure of what a typical person earns.
How does range differ from standard deviation?
Range measures the total spread using only the two extreme values. Standard deviation measures the average distance of all values from the mean. Standard deviation is a much richer measure of variability — a few outliers can inflate range dramatically while barely affecting standard deviation.
What does 'central tendency' mean?
Central tendency refers to measures that describe the center or typical value of a dataset. Mean, median, and mode are all measures of central tendency. They answer the question: around what value does the data cluster?
Advertisement