Descriptive statistics summarize the center, spread and shape of a data set before any modeling begins. Paste a series of values to see a complete statistical profile that matches Excel’s sample formulas.
How it works
Paste a data series to get central tendency, dispersion, quartiles and distribution-shape statistics, matching Excel’s sample formulas.
Mean = Σx ÷ n; Sample variance s² = Σ(x − x̄)² ÷ (n − 1)
Quartiles: linear interpolation (Excel QUARTILE.INC)
Skewness = n ÷ [(n−1)(n−2)] × Σ((x − x̄) ÷ s)³ (Excel SKEW)
Excess kurtosis: Excel KURT definition
Outliers: below Q1 − 1.5·IQR or above Q3 + 1.5·IQRCommon uses
- Exploring KPI and operational data
- Checking data quality before forecasting
- Coursework and research summaries
Worked example
The calculator above opens with this example. Change any input to see the results update instantly, or select Reset to return to these figures.
| Data | 4.2 5.1 3.8 6.0 5.5 4.9 7.2 5.0 4.4 6.3 5.8 4.7 5.2 3.9 6.8 5.4 4.6 5.9 5.1 8.4 4.8 5.6 5.3 4.1 |
| Mean | 5.3333 |
| Standard deviation (sample) | 1.0793 |
| Count (n) | 24 |
| Median | 5.15 |
| Mode | 5.1 |
| Sum | 128 |
| Variance (sample) | 1.1649 |
| Std. dev. (population) | 1.0566 |
Distribution is right-skewed; the median may represent the typical value better than the mean. 1 potential outlier(s) beyond 1.5×IQR: 8.4.
Interpreting the results
- Use the sample standard deviation when the data is a sample; population when it covers every observation.
- The coefficient of variation compares variability across series measured on different scales.
- Positive excess kurtosis means fatter tails than a normal distribution — more extreme values.
Frequently asked questions
Should I use sample or population standard deviation?
Use the sample standard deviation (n − 1) when your data are a sample drawn from a larger population, which is the usual case in business analysis. Use the population version (n) only when the data include every member of the population.
What do skewness and kurtosis indicate?
Skewness measures asymmetry: positive values indicate a longer right tail. Excess kurtosis measures tail heaviness relative to a normal distribution; positive values indicate more extreme observations than a normal distribution would produce.
Which quartile method does the calculator use?
Quartiles are calculated by linear interpolation, the same method as Excel’s QUARTILE.INC and PERCENTILE.INC functions. Other software may use exclusive or nearest-rank methods, which can give slightly different results for small samples.
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