Statistics Calculator: Compute Mean, Median, Mode, and Standard Deviation

Summarizing a data set by hand means sorting values, counting frequencies, and running formulas that are simple in concept but tedious in practice. Our statistics calculator takes a list of numbers and computes all the key descriptive statistics at once — mean, median, mode, variance, standard deviation, and quartiles — so you can focus on interpreting the results rather than crunching numbers.

Key Statistical Measures Explained

Mean (Average)

The mean is the sum of all values divided by the count. It represents the “center of gravity” of your data.

Data: 4, 8, 6, 5, 3, 7, 8, 9
Mean = (4 + 8 + 6 + 5 + 3 + 7 + 8 + 9) / 8
Mean = 50 / 8 = 6.25

The mean is sensitive to outliers. A single extreme value can pull it significantly higher or lower than the typical data point.

Median

The median is the middle value when all values are sorted. If the count is even, it is the average of the two middle values.

Sorted: 3, 4, 5, 6, 7, 8, 8, 9
Middle values: 6 and 7
Median = (6 + 7) / 2 = 6.5

The median is resistant to outliers, making it a better measure of “typical” when your data is skewed. This is why median household income is often more informative than mean household income.

Mode

The mode is the value that appears most frequently. A data set can have no mode (all values unique), one mode (unimodal), or multiple modes (bimodal, multimodal).

Data: 4, 8, 6, 5, 3, 7, 8, 9
Mode = 8 (appears twice)

Mode is the only measure of central tendency that works with non-numeric (categorical) data.

Variance

Variance measures how spread out the values are from the mean. It is the average of the squared differences from the mean.

Data: 4, 8, 6, 5, 3, 7, 8, 9     Mean = 6.25

Differences from mean: -2.25, 1.75, -0.25, -1.25, -3.25, 0.75, 1.75, 2.75
Squared: 5.0625, 3.0625, 0.0625, 1.5625, 10.5625, 0.5625, 3.0625, 7.5625
Population Variance = 31.5 / 8 = 3.9375

Population vs. sample variance: Divide by N for the population variance and by N-1 for the sample variance. The N-1 correction (Bessel’s correction) accounts for the fact that a sample underestimates the true population spread.

Standard Deviation

Standard deviation is the square root of variance. It is expressed in the same units as the original data, making it more interpretable than variance.

Population Std Dev = sqrt(3.9375) = 1.984

A small standard deviation means values cluster tightly around the mean. A large standard deviation means values are widely spread.

Quartiles

Quartiles divide sorted data into four equal parts:

Q1 (25th percentile): The median of the lower half
Q2 (50th percentile): The overall median
Q3 (75th percentile): The median of the upper half
IQR (Interquartile Range): Q3 - Q1, measuring the spread of the middle 50% of data

Sorted: 3, 4, 5, 6, 7, 8, 8, 9
Q1 = 4.5    Q2 = 6.5    Q3 = 8
IQR = 8 - 4.5 = 3.5

The IQR is useful for detecting outliers: any value below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR is considered a potential outlier.

When to Use Each Measure

Situation	Best Measure	Why
Symmetric data, no outliers	Mean	Most informative when data is balanced
Skewed data or outliers present	Median	Resistant to extreme values
Categorical data	Mode	Only option for non-numeric categories
Comparing spread of data sets	Standard deviation	Same units as original data
Detecting outliers	IQR and quartiles	Robust outlier detection method

Practical Use Cases

Academic and Research

Students and researchers use these measures to summarize experimental results, survey responses, and test scores. A professor reporting class performance might show the mean score alongside the median to reveal whether a few very high or low scores are skewing the average.

Business and Finance

Sales teams track the mean and median of deal sizes. A few large enterprise deals can inflate the mean, while the median shows what a “typical” deal looks like. Standard deviation on monthly revenue helps quantify how volatile the business is.

Quality Control

Manufacturing processes monitor the mean and standard deviation of product measurements. If the standard deviation increases, it signals that the process is becoming less consistent, even if the mean stays on target.

Health and Fitness

Tracking workout metrics (heart rate, run times, weights lifted) over time. The mean shows your typical performance, while looking at quartiles reveals how your best and worst sessions compare to your usual range.

How to Use Our Statistics Calculator

Enter your numbers separated by commas, spaces, or line breaks
View all results computed instantly: mean, median, mode, variance, standard deviation, quartiles, and more
Review the sorted data to verify your input
Copy any result with one click

Tips

You can paste data directly from spreadsheets — the tool handles common separators
Enter at least two numbers for meaningful spread statistics
The tool computes both population and sample standard deviation so you can use whichever is appropriate
All calculations run entirely in your browser — your data stays private

Frequently Asked Questions

What is the difference between population and sample standard deviation? Population standard deviation divides by N and describes the entire population. Sample standard deviation divides by N-1 and estimates the population spread from a subset. Use sample when your data represents a subset of a larger group, which is most real-world scenarios.

Can a data set have more than one mode? Yes. If two values tie for the highest frequency, the data is bimodal. If three or more tie, it is multimodal. If every value appears the same number of times, there is no mode.

Why is the median sometimes better than the mean? The median is resistant to outliers. In a data set like 2, 3, 4, 5, 1000, the mean is 202.8 while the median is 4. The median better represents the typical value when extreme observations are present.

What does a standard deviation of zero mean? All values in the data set are identical. There is no variation at all.

How many data points do I need for reliable statistics? For basic descriptive statistics (mean, median), even a handful of values works. For inferential statistics or when computing confidence intervals, 30 or more data points is a common rule of thumb. Quartiles become more meaningful with at least 8 to 10 values.

Try our free Statistics Calculator to compute mean, median, mode, and standard deviation instantly.