How do I interpret skewness and kurtosis values?

Skewness near 0 indicates symmetry; positive values indicate a right tail and negative values a left tail. Excess kurtosis near 0 indicates a normal-like peak; positive (leptokurtic) means heavy tails; negative (platykurtic) means light tails.

How large does my sample need to be for reliable descriptive statistics?

Sample size depends on purpose: n ≥ 30 is a common rule for stable means; for percentiles and tail estimates you need 100 or more. Smaller samples give wide confidence intervals around all summary statistics.

Can I use this calculator for my published research or thesis?

Yes for exploratory analysis and teaching. For formal publications, verify results in peer-reviewed software such as R, Python, SPSS, or SAS. Cite as: STATS UNLOCK. (2026). Descriptive statistics calculator. https://statsunlock.com.

Descriptive Statistics Calculator – Free Online Mean Median Mode SD Tool | StatsUnlock

📥 Data Input

Enter values as comma-separated numbers, paste from a spreadsheet, or upload a file. Each group below becomes a separate cluster summarised independently.

Upload CSV or Excel file

Supports .csv, .txt, .xlsx, .xls — headers detected automatically. Click columns that should each become a cluster — selected columns will be loaded as separate clusters.

Choose a built-in sample dataset

Selecting a dataset replaces the current groups in the Type/Paste tab.

⚙️ Calculation Settings

SD / Variance type

Quartile method

Confidence level for mean CI

Decimal places

📖 Detailed Interpretation of Results

Run the analysis above to populate the detailed interpretation.

✍️ How to Write Your Results in Research

When reporting descriptive statistics in a paper, thesis, or report, choose the format that matches your audience. The five examples below are auto-filled with the values from your most recent run — click 📋 Copy to copy any version directly into your manuscript.

Run the analysis above to auto-fill these reporting examples.

🏁 Conclusion

Run the analysis above to generate a detailed conclusion summarising what these descriptive statistics mean for your data.

🧮 Formulas & Technical Notes

Mean, variance, standard deviation

x̄ = (1/n) · Σᵢ xᵢ s² = (1/(n−1)) · Σᵢ (xᵢ − x̄)² [sample variance] σ² = (1/n) · Σᵢ (xᵢ − x̄)² [population variance] s = √s² [sample SD] SE = s / √n [standard error of the mean] Where: n = sample size xᵢ = each observation x̄ = sample mean s = sample standard deviation σ = population standard deviation SE = standard error of the mean

Median, quartiles, IQR

Sort x in ascending order, then: Q1 = 25th percentile Q2 = 50th percentile (median) Q3 = 75th percentile IQR = Q3 − Q1 Tukey lower fence = Q1 − 1.5·IQR Tukey upper fence = Q3 + 1.5·IQR Linear-interpolation method (Type 7, Excel default): position p = (n − 1) · q + 1 if p is integer → value at that index else → x[⌊p⌋] + (p − ⌊p⌋) · (x[⌊p⌋+1] − x[⌊p⌋])

Skewness & kurtosis (Fisher–Pearson, sample)

m_k = (1/n) · Σ (xᵢ − x̄)^k [k-th central moment] Sample skewness g₁ = m₃ / m₂^(3/2) Adjusted (G1) = √(n(n−1))/(n−2) · g₁ Sample excess kurtosis g₂ = m₄ / m₂² − 3 Adjusted (G2) = ((n−1)/((n−2)(n−3))) · ((n+1)·g₂ + 6) Where: m₂ = variance (population form) m₃ = 3rd central moment m₄ = 4th central moment G1 = bias-corrected skewness (Excel SKEW()) G2 = bias-corrected excess kurtosis (Excel KURT())

Coefficient of variation, SEM, CI

CV = (s / x̄) · 100% SEM = s / √n CI = x̄ ± t_{α/2, n−1} · SEM [t-distribution] (for n ≥ 30 z-distribution gives nearly identical CIs) Where: CV = coefficient of variation, expressed in % SEM = standard error of the mean t = critical t-value at α/2 with df = n − 1

✅ When to Use Descriptive Statistics

This free descriptive statistics calculator is designed for any quantitative dataset where you need to summarise the central tendency, dispersion, and shape before running inferential tests. Use it for class grades, lab measurements, ecological counts, clinical readings, survey scales, or any continuous or count variable.

Decision checklist

Your variable is continuous (interval / ratio) or count
You want a summary before formal hypothesis testing
You want to compare central tendency / spread across clusters
You need APA-ready descriptive statistics for a Methods or Results section
Do NOT use mean / SD on heavily skewed data → use median (IQR) instead
Do NOT report mode for continuous data unless data are binned
Do NOT use these statistics for nominal-only data → use frequency tables

Real-world examples

Education. Comparing exam-score distributions across three teaching cohorts (mean, SD, range, skewness).
Medicine / Clinical. Reporting baseline systolic blood pressure (M, SD, 95% CI) for placebo vs drug arms.
Ecology / Wildlife. Summarising tree diameter at breast height across multiple field sites for forest structure analysis.
Psychology. Reaction-time descriptives (median, IQR) by morning vs evening sessions where data are often right-skewed.

Sample size guidance

n < 10 — descriptive estimates are unstable; report all values.
n = 10–30 — central tendency reasonably stable; tail estimates (skew, kurtosis) noisy.
n ≥ 30 — mean and SD become reliable; CIs narrow.
n ≥ 100 — percentiles and tail behaviour become trustworthy.

🧭 How to Use This Descriptive Statistics Calculator

Enter your data in the Type/Paste tab as comma-separated numbers (e.g. 52, 48, 55, 61, 47, ...). Each cluster goes in its own card.
Rename the cluster by clicking the green title field — Group / Cluster names are fully editable.
Add more clusters by clicking ＋ Add Another Group / Cluster. Remove any cluster with the trash icon.
Or upload a CSV / Excel file. Click numeric column buttons; each clicked column becomes a separate cluster.
Or pick a built-in sample dataset from the Sample Datasets tab.
Configure sample vs population SD, quartile method, confidence level, and decimal places.
Click ▶ Run Descriptive Statistics.
Review the summary cards, per-cluster table, full statistics table, and the four visualisations.
Read the dynamic Interpretation, How-to-Write-Your-Results examples, and the Conclusion.
Export via Download Doc, Download PDF, or Copy Summary for your manuscript.

❓ Frequently Asked Questions

Q1. What is descriptive statistics and when should I use it?

Descriptive statistics summarise the central tendency, dispersion, and shape of a dataset using values such as mean, median, standard deviation, variance, skewness, and kurtosis. Use them whenever you need to describe what your data look like before any inferential analysis.

Q2. What is the difference between mean, median, and mode?

The mean is the arithmetic average, the median is the middle value when data are sorted, and the mode is the most frequent value. Mean is sensitive to outliers, median is robust, and mode is most useful for categorical or discrete data.

Q3. What is the difference between sample and population standard deviation?

The sample SD divides by (n − 1) and gives an unbiased estimate of the population SD when you have only a sample. The population SD divides by n and is used only when the data cover the whole population. This calculator defaults to sample SD; switch to population in Settings.

Q4. How do I interpret skewness and kurtosis?

Skewness near 0 means symmetric; positive skew = right tail, negative = left tail. Excess kurtosis near 0 means normal-like; positive (leptokurtic) = heavy tails / sharp peak; negative (platykurtic) = light tails / flat peak.

Q5. What is the IQR and why is it useful?

The interquartile range (IQR = Q3 − Q1) measures the spread of the middle 50% of the data. It is robust to outliers and is the basis of Tukey's 1.5×IQR rule for outlier detection.

Q6. What is the coefficient of variation and when is it used?

CV = SD/mean × 100% expresses variability relative to the mean. It allows comparison of dispersion between datasets with different units or very different scales. CV is undefined when the mean is zero.

Q7. Should I report mean ± SD or median (IQR)?

Use mean ± SD for approximately normal data, and median (IQR) for skewed or non-normal data. Look at the histogram, skewness, and Q–Q plot above to decide. When in doubt, report both.

Q8. How large must my sample be for reliable descriptive statistics?

n ≥ 30 is a useful rule of thumb for stable means and standard deviations. Percentiles and skewness/kurtosis need much more — typically 100+ — to be trustworthy.

Q9. How do I report descriptive statistics in APA 7th edition?

Combine central tendency and dispersion: e.g., "Participants reported moderate scores (M = 53.40, SD = 8.21, n = 30)." For non-normal data: "Mdn = 52.50, IQR = [48, 58]". Always state the unit and sample size.

Q10. Can I cite this calculator in a published paper?

Yes — for exploratory work and teaching. For formal publication, verify results in peer-reviewed software (R, Python, SPSS, SAS) and cite as: STATS UNLOCK. (2026). Descriptive statistics calculator. https://statsunlock.com/descriptive-statistics-calculator

📚 References

The following references support the methods used in this descriptive statistics calculator, covering mean, median, mode, standard deviation, skewness and kurtosis, and best practices in quantitative research methods and APA-style reporting.

Tukey, J. W. (1977). Exploratory data analysis. Addison-Wesley.
Pearson, K. (1895). Contributions to the mathematical theory of evolution — II. Skew variation in homogeneous material. Philosophical Transactions of the Royal Society A, 186, 343–414. https://doi.org/10.1098/rsta.1895.0010
Joanes, D. N., & Gill, C. A. (1998). Comparing measures of sample skewness and kurtosis. Journal of the Royal Statistical Society: Series D (The Statistician), 47(1), 183–189. https://doi.org/10.1111/1467-9884.00122
Hyndman, R. J., & Fan, Y. (1996). Sample quantiles in statistical packages. The American Statistician, 50(4), 361–365. https://doi.org/10.1080/00031305.1996.10473566
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). SAGE Publications.
Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the behavioral sciences (10th ed.). Cengage Learning.
Howell, D. C. (2013). Statistical methods for psychology (8th ed.). Cengage Learning.
American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). APA. https://doi.org/10.1037/0000165-000
Wilcox, R. R. (2017). Introduction to robust estimation and hypothesis testing (4th ed.). Academic Press. https://doi.org/10.1016/C2015-0-01807-7
R Core Team. (2024). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org/
Virtanen, P., Gommers, R., Oliphant, T. E., et al. (2020). SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods, 17, 261–272. https://doi.org/10.1038/s41592-020-0772-5
NIST/SEMATECH. (2013). e-Handbook of statistical methods. National Institute of Standards and Technology. https://www.itl.nist.gov/div898/handbook/
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
Kim, H.-Y. (2013). Statistical notes for clinical researchers: Assessing normal distribution (2) using skewness and kurtosis. Restorative Dentistry & Endodontics, 38(1), 52–54. https://doi.org/10.5395/rde.2013.38.1.52