Statistics Calculator
Full descriptive statistics for a dataset: centre, spread, quartiles, skew and outliers.
About Statistics Calculator
Descriptive statistics summarise a dataset without assuming any distribution. The mean is the arithmetic average; the median is the middle value; the mode is the most frequent value (or no mode when all values are unique). Spread is captured by the range, variance and standard deviation. Quartiles divide the sorted data into four equal parts, and the IQR (Q3−Q1) is the middle 50 %. Tukey fences sit at Q1−1.5×IQR and Q3+1.5×IQR; any point outside them is flagged as an outlier. Skewness measures distributional asymmetry; excess kurtosis measures tail heaviness relative to a normal distribution.
Formulas
Mean
Mean = (sum of all values) / n
- n
- Number of values
- x_i
- Each value
Sample variance
Sample variance = Σ(xᵢ − x̄)² / (n−1)
- x̄
- Mean
- n
- Count
Tukey fences
Lower fence = Q1 − 1.5·IQR; Upper fence = Q3 + 1.5·IQR
- IQR
- Q3 − Q1
Worked example
With the default values below, Statistics Calculator returns Mean of 6.8000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Dataset
- 4, 7, 13, 2, 1, 7, 9, 15, 3, 7
- Dataset typeone of Sample (divide by n−1), Population (divide by n)
- Sample (divide by n−1)
Results
- Count (n)
- 10
- Sum
- 68.0000
- Mean
- 6.8000
- Median
- 7.0000
- Mode
- 7
- Range
- 14.0000
- Minimum
- 1.0000
- Maximum
- 15.0000
- Variance
- 21.0667
- Std Deviation
- 4.5898
- Std Error
- 1.4514
- Q1 (25th pct)
- 3.2500
- Q2 / Median
- 7.0000
- Q3 (75th pct)
- 8.5000
- IQR
- 5.2500
- Lower Fence
- -4.6250
- Upper Fence
- 16.3750
- Outliers
- None
- SkewnessPositive = right tail; negative = left tail.
- 0.6002
- Excess Kurtosis0 for normal; positive = heavy tails.
- -0.4273
Step by step
- 1Dataset= n = 10 values
- 2Mean= 6.8000
- 3Variance= 21.0667
- 4Std deviation= 4.5898
- 5Quartiles= IQR = 5.2500
- 6Tukey fences= 0 outlier(s)
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
When should I choose population vs. sample variance?
Choose sample (÷ n−1, Bessel's correction) when your data is a subset drawn from a larger population — the typical research scenario. Choose population (÷ n) only when your dataset contains every element of the population you care about, such as the grades of all 30 students in a specific class.
What does it mean if there is no mode?
When every value appears exactly once, no value is more frequent than any other, so the dataset has no mode. Some textbook definitions force a mode in that case, but it conveys no useful information. This calculator honestly reports 'No mode' rather than inventing one.
How are outliers detected?
This calculator uses Tukey fences: any data point below Q1−1.5×IQR or above Q3+1.5×IQR is classified as an outlier. This is the standard method used by box-and-whisker plots. For datasets with heavier tails you might apply a stricter 3×IQR rule, but 1.5 is the default.
What does excess kurtosis tell me?
Excess kurtosis compares the tail weight of your distribution to a normal distribution (which has excess kurtosis = 0). A positive value means heavier tails and more extreme values are likely; a negative value means lighter tails. It requires at least 4 data points to compute.