What is the Mean?
The mean (arithmetic average) is the sum of all values divided by the number of values. It's the most widely used measure of central tendency in statistics.
x̄ = (x₁ + x₂ + ... + xₙ) / n = Σx / n
Quick Example
Dataset: 5, 8, 12, 15, 20
Sum = 5 + 8 + 12 + 15 + 20 = 60
Mean = 60 ÷ 5 = 12
What Does This Calculator Compute?
Enter any dataset to instantly get:
Mean
Sum ÷ count
Median
Middle value
Mode
Most frequent value
Standard Deviation
Spread from mean
Variance
Squared std dev
Range, Min, Max, Sum
Full summary stats
Formulas Used
| Statistic | Formula |
|---|---|
| Mean | x̄ = Σx / n |
| Median | Middle value (sorted). Average of two middle values if even n |
| Mode | Most frequently occurring value(s) |
| Variance (pop.) | σ² = Σ(xᵢ − x̄)² / n |
| Std Dev (pop.) | σ = √[Σ(xᵢ − x̄)² / n] |
| Range | Range = max − min |
Pro Tip: When comparing the mean and median, if they're very different, your data is likely skewed or contains outliers. The median is more robust in such cases.
Example Dataset
Let's analyze a sample of 10 student test scores:
78, 85, 92, 65, 88, 74, 90, 82, 78, 95
Mean
82.70
Median
83.50
Mode
78
Std Dev
9.21
FAQ
Is this calculator using population or sample standard deviation?
This calculator computes population standard deviation (divides by n). For small samples, you'd typically want sample standard deviation (divides by n−1). The difference is small for large datasets but more significant for small samples. Both formulas are shown in the results section.
How many numbers can I enter?
You can enter as many numbers as you need — there's no practical limit. The calculator runs entirely in your browser and handles datasets with hundreds or thousands of values easily.
Can I enter negative numbers or decimals?
Yes! The calculator handles negative numbers (e.g., −5, −12.3) and decimal values (e.g., 3.14, 0.5) without any issues. Just separate values with commas.
What does it mean when the mode shows "No mode"?
This appears when every value in the dataset is unique (no value appears more than once). In this case, no mode exists because no value is "most frequent."
What's the difference between mean and median?
The mean is the arithmetic average (sum ÷ count). The median is the middle value. When data contains outliers or is heavily skewed, the mean is pulled in the direction of the outlier while the median stays near the "typical" value. For example, house prices and incomes are almost always reported using the median for this reason.