Statistics Calculator
Paste your numbers on the left and pick sample or population; the mean, median, standard deviation and other key statistics appear on the right, with a histogram below to show the distribution.
Data
Enter numbers to calculate statistics instantly.
Key statistics
- Median
- —
- Mode
- —
- Standard deviation (SD)
- —
- Variance
- —
- Minimum
- —
- Maximum
- —
- Range
- —
- Standard error (SE)
- —
- Coefficient of variation (CV)
- —
- 95% confidence interval
- —
This calculator reports descriptive statistics for the data you enter. Small samples or many outliers reduce how representative the summary is, and the 95% confidence interval uses a normal (large-sample) approximation.
Distribution
See where the values cluster and how far they spread.
- Lower 25% (Q1)
- —
- Median (Q2)
- —
- Upper 25% (Q3)
- —
- Middle 50% width (IQR)
- —
- Outliers
- —
A taller bar means more values in that range. A lone bar at one end may be an outlier.
ready to use.
- Visible firstKeep the input and result positions clear.
- Results firstPut the main number up front and keep the process secondary.
- Less to askNo sign-up or extra information before using the tool.
Reading summary statistics without misreading them
Statistics is about reducing many numbers to a few summary values so the data becomes understandable. This screen splits that work into the input on the left, the key statistics on the right, and a histogram below.
The results are descriptive statistics that summarize the data you entered — not causation, prediction or hypothesis testing — and the confidence interval is a normal approximation.
One screen for the summary values
Paste numbers and the tool reports center (mean, median, mode), spread (standard deviation, variance, range, IQR) and outliers together. Reading different views side by side keeps you from misreading the data.
- Center: mean, median, mode
- Spread: standard deviation, variance, range, IQR
- Position and extremes: quartiles, outliers
The order to read input and result
Paste separated numbers on the left and pick sample or population. The mean and key statistics update on the right, and the quartiles, outliers and histogram below show the distribution. There is no Calculate button.
When the mean and median differ
The mean adds every value and divides, so it is pulled by outliers; the median is the middle value and resists them. A large gap between the two is a sign the distribution is skewed.
Standard deviation, variance, CV
Variance is the average squared deviation; the standard deviation is its square root, so it reads in the original units. The coefficient of variation (CV) divides the SD by the mean to compare spread across data of different scales.
- Variance = average squared deviation (n−1 for a sample)
- Standard deviation = √variance
- CV = standard deviation ÷ mean × 100%
Reading the shape with a histogram
A histogram splits the value range into bins and shows the count in each as a bar height. Bars clustered in the middle mean values sit near the mean; a long tail on one side means values are scattered that way.
Sample vs population, and the limits
Pick population (n) when the data is the whole group and sample (n−1) when it is a subset. These values are descriptive statistics, not causation or prediction, and the confidence interval is a normal approximation.
- Descriptive statistics, not causation or prediction
- Confidence interval is a normal (large-sample) approximation
- Small samples and strong skew need careful reading
Common questions about the statistics calculator
What is the difference between sample and population standard deviation?
The sample version divides the sum of squared deviations by n−1 (Bessel’s correction) so it underestimates the population variance less; the population version divides by n. Choose “Population” when your data is the whole group of interest and “Sample” when it is a subset drawn from a larger group.
How are the quartiles and IQR calculated?
The values are sorted, then the 25%, 50% and 75% positions are found by linear interpolation (the same method as a spreadsheet’s PERCENTILE.INC) and shown as Q1, Q2 and Q3. The IQR is Q3−Q1, the spread of the middle 50%.
How are outliers flagged?
Values below Q1−1.5×IQR or above Q3+1.5×IQR are flagged as outliers (Tukey’s fences). This is not proof of an error — it is a signal that the value is worth checking.
Should I read the mean or the median?
The mean is sensitive to outliers, while the median resists extreme values. When the two differ a lot, the distribution is skewed, so read the median alongside the mean.
How accurate is the 95% confidence interval?
It uses the normal (large-sample) approximation, mean ± 1.96 × standard error. For small samples it can differ from a t-distribution based interval.
Reviewed 2026-07-14. Quartiles use linear interpolation (percentiles); outliers use the 1.5×IQR fences.