Standard Deviation Calculator - Complete Statistical Analysis

Calculate standard deviation, variance, mean, median, mode, quartiles, and other statistical measures. Support for both population and sample data with detailed explanations.

Data Input

Manual Input

Population

Use when you have data for the entire population

Sample

Use when you have sample data from a larger population

Data Visualization


Histogram and Box Plot will be displayed here
Enter data and calculate to see visualization

Statistical Analysis

Outlier Detection

Values outside 1.5 × IQR from Q1 and Q3 are considered outliers:

Lower Bound = Q1 - 1.5 × IQR Upper Bound = Q3 + 1.5 × IQR
Coefficient of Variation

Measures relative variability:

CV = (σ / μ) × 100%

Statistical Formulas

Population Standard Deviation

Used when you have data for the entire population:

σ = √(Σ(x - μ)² / N)

Where: σ = standard deviation, μ = mean, N = population size

Sample Standard Deviation

Used when working with a sample from a larger population:

s = √(Σ(x - x̄)² / (n - 1))

Where: s = sample standard deviation, x̄ = sample mean, n = sample size

Variance

The square of standard deviation:

Population Variance: σ² = Σ(x - μ)² / N Sample Variance: s² = Σ(x - x̄)² / (n - 1)
Other Statistical Measures
Mean: μ = Σx / n Median: Middle value when data is sorted Mode: Most frequently occurring value Range: Maximum - Minimum

How to Use the Standard Deviation Calculator

Step 1: Enter Your Data

Input your numbers separated by commas, spaces, or line breaks. You can also use our sample data sets to get started.

Step 2: Choose Population or Sample

Select "Population" if you have data for the entire group, or "Sample" if your data represents a subset of a larger population.

Step 3: Calculate Results

Click the calculate button to get standard deviation, variance, mean, median, mode, and other statistical measures.

Step 4: Analyze Results

Review the comprehensive statistical analysis including outlier detection and coefficient of variation.