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Data Processing

General Statistics Calculator

· Last updated:2026-09-19

Paste one or two columns of numbers and get the complete descriptive suite — mean/median/mode, sample and population variance, type-7 quartiles and percentiles, MAD, adjusted skewness and kurtosis, Tukey outliers — plus covariance, Pearson r, tie-corrected Spearman rho and least-squares regression for two columns.

Details

What this tool helps you do

Every quantity is computed from the standard formulas, with the conventions statisticians actually argue about made explicit. Quartiles and percentiles use R’s default "type 7" linear interpolation: h = (n − 1)·p + 1 on the sorted sample, so Q1/Q3 match what R, pandas and Excel’s PERCENTILE.INC produce. Variance and standard deviation are reported in both flavours — sample (divide by n − 1, the unbiased estimator for a sample) and population (divide by n) — and the variance-basis switch decides which one drives the coefficient of variation and the standard error of the mean. Shape statistics follow the moment conventions: skewness comes both as the biased moment ratio g1 = m3/m2^(3/2) and as the adjusted Fisher–Pearson G1 = √(n(n−1))/(n−2)·g1 that Excel’s SKEW returns; kurtosis is excess (normal = 0), both biased g2 = m4/m2² − 3 and the small-sample-adjusted G2. Outliers use Tukey’s fences (Q1 − 1.5·IQR, Q3 + 1.5·IQR) from the same type-7 quartiles. When you paste a second column, the calculator adds the bivariate suite: sample covariance, Pearson’s r on the raw pairs, Spearman’s rho computed as Pearson on average-assigned ranks (the tie-correct definition — the 6Σd² shortcut is wrong once ties exist), and the least-squares line ŷ = slope·x + intercept with R². Input accepts any mix of spaces, commas, semicolons and tabs, plus scientific notation; tokens that are not valid numbers are rejected up front rather than silently dropped.

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Written by the Elysia Tools team

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Data Processing
Input types
textarea, select, number, checkbox
Output type
html
Sample coverage
4
API ready
Yes

Overview

The General Statistics Calculator provides comprehensive univariate and bivariate statistical analysis from raw numerical data. Paste one or two datasets separated by spaces, commas, semicolons, or line breaks to instantly compute measures of central tendency, sample and population dispersion, Type-7 quartiles, adjusted skewness and kurtosis, Tukey outliers, and least-squares linear regression.

When to use

  • Analyzing central tendency, spread, and shape characteristics across a single set of measurements.
  • Detecting anomalous data points and extreme deviations using standard Tukey interquartile range fences.
  • Evaluating linear and monotonic relationships between two paired variables via Pearson r, Spearman rho, and regression modeling.

How it works

  1. 1Paste or type numbers into the primary dataset field using spaces, commas, semicolons, tabs, or newlines as delimiters.
  2. 2Optionally enter an equal-length second series into the comparison field for bivariate correlation and linear regression analysis.
  3. 3Select the variance calculation basis (Sample n−1 or Population n) and set the desired decimal precision up to 6 places.
  4. 4Review the generated report covering summary statistics, percentiles, distribution moments, outlier lists, and trendline equations.

Use cases

  • Quality control testing to verify manufacturing tolerances and detect extreme defect outliers.
  • Academic research data analysis requiring standard descriptive tables with exact Fisher-Pearson skewness and excess kurtosis.
  • Financial or sales data exploration comparing paired metric series for correlation and regression slope calculation.

Examples

1. Univariate Summary and Outlier Detection

Quality Assurance Analyst

Background

A QA analyst needs to assess weight deviations across a production batch and flag any measurements falling outside expected fences.

Problem

Calculate sample dispersion parameters and locate values exceeding standard Tukey outlier limits.

How to use

Enter the batch measurement values into the Numbers field, choose 'Sample (n−1)' as the variance basis, and set decimal places to 4.

numbers: '2 4 4 4 5 5 7 9', varianceBasis: 'sample', decimalPlaces: 4, showOutliers: true

Outcome

Produces a mean of 5.0000, median of 4.5000, sample standard deviation of 2.1381, Q1/Q3 of 4.0000/5.5000, and identifies 9 as an upper outlier above the 7.75 fence.

2. Bivariate Correlation and Regression

Data Analyst

Background

An analyst wants to quantify the relationship between advertising spend and conversion volume across multiple campaigns.

Problem

Determine Pearson and Spearman correlation coefficients and derive the best-fit linear regression equation.

How to use

FAQ

How does this tool calculate quartiles and percentiles?

It implements R's default Type-7 linear interpolation formula, matching outputs generated by R, pandas, and Excel's PERCENTILE.INC function.

What is the difference between sample and population variance modes?

Sample variance divides sum of squares by n−1 as an unbiased estimator for sample data, whereas population variance divides by n.

How are statistical outliers identified?

Outliers are determined using Tukey's fences at Q1 − 1.5·IQR for the lower threshold and Q3 + 1.5·IQR for the upper threshold.

How does Spearman's rho handle duplicate or tied values?

Spearman's rho applies Pearson's correlation formula directly to average-assigned ranks, maintaining accurate results in the presence of tied data.

What input formats and character delimiters are supported?

Input accepts numbers formatted with spaces, commas, semicolons, tabs, newlines, and standard scientific notation.

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Enter input values into Numbers and the corresponding output values into the Comparison dataset, selecting 'Population (n)' for the variance basis.

numbers: '1, 2, 3, 4, 5', datasetB: '3, 5, 7, 9, 11', varianceBasis: 'population', decimalPlaces: 4, showOutliers: true

Outcome

Returns Pearson r of 1.0000, tie-corrected Spearman rho of 1.0000, R² of 1.0000, and the linear regression line ŷ = 2.0000·x + 1.0000.