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FREE ADVANCED STATISTICS CALCULATOR

Statistics calculator for standard deviation, variance, quartiles, and regression.

Calculate mean, median, mode, sample or population standard deviation, variance, quartiles, IQR, frequency tables, grouped data estimates, correlation, and linear regression from one focused workspace.

DATA WORKSPACE

Input and options

sample
Select the results you want

RESULT

Ready

No data
σ

Choose a data type, select the statistics you need, then calculate.

STATISTICS FORMULAS EXPLAINED

Understand the result before you use it.

This statistics calculator is built for class assignments, research summaries, lab data, and business reports where users need both a number and a clear method. Choose the data format first, then decide whether the problem needs sample or population statistics.

STANDARD DEVIATION

Sample vs population SD

Use sample standard deviation when your values are only part of a larger group. Use population standard deviation when the values are the complete population being studied.

VARIANCE

Average squared spread

Variance measures average squared distance from the mean. Standard deviation is the square root of variance, so it is easier to read in the original unit.

QUARTILES AND IQR

Middle spread of the data

Q1, Q3, and IQR help explain spread without being controlled by very large or very small values. IQR is useful when checking possible outliers.

FREQUENCY TABLES

Repeated values and grouped intervals

Use discrete frequency rows when exact values repeat. Use grouped data when values are already summarized into class intervals such as 10–20 or 20–30.

LINEAR REGRESSION

Paired X/Y relationship

Paired mode calculates slope, intercept, correlation, R², covariance, and an optional predicted y-value for a selected x-value.

OUTLIERS

1.5 × IQR rule

The outlier count uses the common IQR fence method: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are flagged as possible outliers.

WORKED EXAMPLE

How sample standard deviation is calculated.

For the raw data set 58, 64, 72, 72, 78, 84, 91, the mean is about 74.14. With sample mode selected, the calculator divides the squared deviations by n − 1.
Sample variances² = Σ(x − x̄)² ÷ (n − 1)

For the example data, sample variance is about 128.14.

Sample standard deviations = √128.14 ≈ 11.32

The typical distance from the mean is about 11.32 data units.

Population standard deviationσ = √(Σ(x − μ)² ÷ n)

Use this only when your entered values are the full population.

COMMON QUESTIONS

Quick answers for statistics problems.

What is the formula for sample standard deviation?

Subtract the mean from each value, square each difference, add them, divide by n − 1, then take the square root.

What is the difference between variance and standard deviation?

Variance is squared spread. Standard deviation is the square root of variance, so it is easier to compare with the original data unit.

When should I use grouped data?

Use grouped data when you only have class intervals and frequencies. The calculator estimates mean and spread using each class midpoint.

Can this calculator do linear regression?

Yes. Choose paired X/Y mode to calculate slope, intercept, correlation r, R², covariance, and optional prediction.

Read the standard deviation formula guide →Use Graphing Calculator for visual checks →

ABOUT THIS TOOL

Statistics Calculator

Analyse raw data, frequency tables, grouped intervals, or paired X/Y values using descriptive statistics, sample and population standard deviation, variance, quartiles, IQR, outlier checks, and regression results.

  • Calculate sample or population standard deviation and variance from raw values
  • Find mean, median, mode, range, quartiles, IQR, percentiles, and outliers
  • Use frequency tables, grouped class intervals, and paired X/Y regression data

KEY FUNCTIONS

Raw data, frequency table, grouped data, and paired X/Y input modesSample and population standard deviation optionsVariance, mean, median, mode, range, quartiles, IQR, percentile, CV, skewness, and outlier countLinear regression slope, intercept, correlation r, R², covariance, and predictionDistribution bars for entered valuesSelectable result metrics to keep the output focused
Browse math & algebra tools →

LEARN THE METHOD

Guides for this calculator workflow

GUIDEStandard deviation formulaCompare sample and population standard deviation, variance, mean deviations, quartiles, and spread.Read →GUIDEHow to choose a statistical testSeparate descriptive statistics, t-tests, correlation, and one-way ANOVA by the question and data type.Read →GUIDETI-84 style online calculator workflowsUse independent online workflows for graphing equations, tables, trace values, roots, intersections, scientific calculations, matrices, statistics, and unit conversion.Read →

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