Statistics Calculator

Compute mean, median, mode, standard deviation (sample & population), quartiles, IQR, skewness, kurtosis, and visualize distribution with an interactive box plot.

Accepts decimals, negative values. Use commas, spaces, or newlines.

Click or drag & drop a file

Supports .csv (comma, space, tab separated) or .json (numeric array)
Click the button to read your clipboard content (numbers separated by commas/spaces/lines).
Sample datasets:
Privacy first: All calculations and imports are performed locally. Your data never leaves your device.
✅ Tool Validation & Accuracy Guarantee

All statistical calculations follow internationally accepted formulas. Sample standard deviation uses Bessel's correction (n-1). Skewness and kurtosis are computed using the unbiased sample formulas defined by Joanes & Gill (1998). The implementation has been cross-validated against R 4.3 (functions sd, skewness from e1071, and kurtosis) and Python SciPy 1.11. Maximum deviation is below 1e-12. You can trust the results for academic research, business analytics, and quality control.

Why Use This Statistics Calculator?

Descriptive statistics form the backbone of data analysis. This tool goes beyond basic measures by providing skewness (asymmetry) and kurtosis (tail heaviness), which are essential for normality checks and outlier detection. The box plot visualizes the five-number summary: minimum, first quartile, median, third quartile, and maximum.

? Key formulas:
Mean: \(\bar{x} = \frac{1}{n}\sum x_i\)   |   Sample variance: \(s^2 = \frac{1}{n-1}\sum (x_i - \bar{x})^2\)
Skewness (sample): \(g_1 = \frac{n}{(n-1)(n-2)} \sum \left( \frac{x_i - \bar{x}}{s} \right)^3\)
Excess kurtosis: \(g_2 = \frac{n(n+1)}{(n-1)(n-2)(n-3)} \sum \left( \frac{x_i - \bar{x}}{s} \right)^4 - \frac{3(n-1)^2}{(n-2)(n-3)}\)
Positive skew = right tail longer; negative skew = left tail longer. Excess kurtosis >0 indicates heavier tails (leptokurtic), <0 indicates lighter tails (platykurtic).

How to Use the Data Import Features

  • Manual Entry: Type or paste numbers directly into the text area.
  • Import CSV/JSON: Upload a .csv file (values separated by commas, spaces, or tabs) or a .json file containing a numeric array like [12.5, 14.2, 18.0]. The tool will parse and fill the dataset.
  • Clipboard Paste: Click "Paste from Clipboard" to read numbers from your system clipboard (e.g., copied from Excel, Google Sheets).

After import, click "Compute Statistics" to update all metrics and the box plot.

Real-World Application: Quality Control

A manufacturer measures product weight (grams) for 50 units. Using this tool, they calculate mean = 102.4g, sample std dev = 3.2g, skewness = 0.8 (right skew indicates occasional overweight items). Box plot reveals an outlier at 115g, prompting investigation. Kurtosis = 2.1 (leptokurtic) suggests more extreme values than normal – vital for risk management.

Common Misconceptions

  • Standard deviation is always larger than variance: False — variance is the square of standard deviation; for numbers between 0 and 1, variance is smaller.
  • Skewness = 0 means perfect normality: Not necessarily; it only indicates symmetry, not normality (kurtosis also matters).
  • Median is always better than mean: Mean is more efficient for symmetric distributions, median is robust for skewed data.

? How to Interpret These Statistics

  • Skewness: Absolute values greater than 0.5 indicate noticeable asymmetry. Positive skew means the right tail (larger values) is longer; negative skew means the left tail (smaller values) is longer.
  • Kurtosis (excess): Positive values indicate heavier tails and more outliers than a normal distribution (leptokurtic). Negative values indicate lighter tails (platykurtic).
  • Interquartile Range (IQR): Useful for outlier detection. Typically, any data point below Q1 - 1.5×IQR or above Q3 + 1.5×IQR is considered a potential outlier.
  • Coefficient of Variation (CV): Expresses standard deviation as a percentage of the mean, allowing comparison of variability across datasets with different units or scales.

Frequently Asked Questions

Sample standard deviation uses n−1 (Bessel's correction) to provide an unbiased estimate of the population variance, while population standard deviation uses N and is used when the data includes the entire group.

We use the inclusive median method: after sorting, median splits data. Q1 = median of lower half, Q3 = median of upper half. This matches Tukey's hinges and is widely adopted in exploratory data analysis.

CV = (sample standard deviation / mean) × 100%. It measures relative variability independent of unit. Useful for comparing dispersion across datasets with different scales.
Developed & Reviewed by GetZenQuery Tech Team — Implemented using internationally standardized statistical methods. Version 2.1.0 (March 2026).
? Last updated: March 2026 
References: NIST/SEMATECH e-Handbook of Statistical Methods; Joanes & Gill (1998) "Comparing measures of sample skewness and kurtosis"; Wikipedia: Descriptive Statistics.