# General Statistics Calculator

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.

> Canonical page: https://elysiatools.com/en/tools/general-statistics-calculator

- **Category:** Data Processing

- **Keywords:** statistics calculator, descriptive statistics, mean median mode, variance, standard deviation, quartiles, percentile, iqr, skewness, kurtosis, outliers, pearson correlation, spearman, linear regression, covariance

## Overview

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.

## Inputs

- **Numbers** (textarea): e.g. 2 4 4 4 5 5 7 9 — spaces, commas, semicolons, tabs or new lines; scientific notation ok
- **Comparison dataset (optional)** (textarea): optional second column for correlation and regression (same number of values)
- **Variance basis** (select)
- **Decimal places** (number)
- **Show outliers** (checkbox)

## 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

- Paste or type numbers into the primary dataset field using spaces, commas, semicolons, tabs, or newlines as delimiters.
- Optionally enter an equal-length second series into the comparison field for bivariate correlation and linear regression analysis.
- Select the variance calculation basis (Sample n−1 or Population n) and set the desired decimal precision up to 6 places.
- Review 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.

## Frequently asked questions

### 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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