Descriptive Statistics Calculator
Instantly compute mean, median, mode, range, variance, and standard deviation for any dataset. Paste in your numbers and choose sample or population — results.
Added May 15, 2026
Input
Example: 2, 4, 4, 4, 5, 5, 7, 9
Use 'Sample' when your data is a subset of a larger population (the common default). Use 'Population' when your data is the entire group.
Result
Enter a value for dataset to see your result.
How it works
Computes the full set of descriptive statistics — mean, median, mode, range, variance, and standard deviation — for any list of numbers you paste in.
Formula
Mean = Σx / n Variance (sample) = Σ(x − x̄)² / (n − 1) SD = √Variance
- n
- Number of data points
- x̄
- Sample mean (average of all values)
- Σ(x − x̄)²
- Sum of squared deviations from the mean
- SD
- Standard deviation — average spread from the mean
Step by step
- 01Paste or type your numbers, separated by commas, spaces, or line breaks.
- 02The mean is the sum of all values divided by the count.
- 03The median is the middle value when the data is sorted (or the average of the two middle values for even-length datasets).
- 04Mode is the value that appears most often; if all values are unique there is no mode.
- 05Range = Maximum − Minimum.
- 06Variance measures spread: square each deviation from the mean, sum them, then divide by n−1 (sample) or n (population).
- 07Standard deviation is the square root of variance — it's in the same units as your data.
Examples
Classic statistics example: 2, 4, 4, 4, 5, 5, 7, 9 (population)
Eight values with a mean of 5. The value 4 appears three times (mode). Population standard deviation is exactly 2.
Inputs
- Dataset:
- 2, 4, 4, 4, 5, 5, 7, 9
- Variance & SD type:
- population
Result
- Count (n):
- 8
- Mean (average):
- 5
- Median:
- 4.5
- Minimum:
- 2
- Maximum:
- 9
- Range:
- 7
- Variance:
- 4
- Standard Deviation:
- 2
Simple 5-value sample: 10, 20, 30, 40, 50
Five evenly spaced values. Mean and median are the same (30). Sample variance = 250, standard deviation ≈ 15.81.
Inputs
- Dataset:
- 10, 20, 30, 40, 50
- Variance & SD type:
- sample
Result
- Count (n):
- 5
- Mean (average):
- 30
- Median:
- 30
- Minimum:
- 10
- Maximum:
- 50
- Range:
- 40
Frequently asked questions
What is the difference between sample and population standard deviation?
Population SD divides by n (the full count) and is used when your data covers every member of the group. Sample SD divides by n−1 (Bessel's correction) and is used when your data is a subset — it provides an unbiased estimate of the true population SD. When in doubt, use sample SD.
What if there is no mode?
If every value appears exactly once, there is no mode — the calculator will say 'No mode — all values unique'. If multiple values tie for the highest frequency, all of them are modes (a multimodal dataset).
How is the median calculated for an even number of values?
Sort the values. If the count is odd, the median is the middle value. If even, the median is the average of the two middle values. For example, [1, 2, 3, 4] has a median of (2+3)/2 = 2.5.
Can I enter negative numbers or decimals?
Yes. The calculator handles any real numbers — positive, negative, zero, and decimals. Separate them with commas, spaces, or line breaks.
What does standard deviation tell me?
Standard deviation measures how spread out your data is around the mean. A small SD means values cluster tightly around the mean; a large SD means they are spread out. For normally distributed data, about 68% of values fall within ±1 SD of the mean.