What is Variance in Statistics?

Variance is a statistical measurement of the spread between numbers in a data set. It measures how far each number in the set is from the mean and thus from every other number in the set. Variance is often represented by σ² for population variance and s² for sample variance.

What is the difference between Population Variance and Sample Variance?

Population variance (σ²) uses all data points from the entire population with denominator N, while sample variance (s²) uses data from a sample of the population with denominator n-1 (Bessel's correction) to provide an unbiased estimate of the population variance.

How to calculate variance step by step?

1. Calculate the mean of the data set. 2. Subtract the mean from each data point (deviation). 3. Square each deviation. 4. Sum all squared deviations. 5. Divide by N for population variance or n-1 for sample variance.

What are the different methods to calculate variance?

Two main methods: 1. Direct Method: Uses actual mean to calculate deviations. 2. Assumed Mean Method (Short-cut Method): Uses an assumed mean to simplify calculations, especially for large data sets.

प्रसरण क्या होता है?

प्रसरण (Variance) आँकड़ों के एक समूह में फैलाव का माप है। यह दर्शाता है कि प्रत्येक आँकड़ा माध्य से कितना दूर है। प्रसरण जितना अधिक होगा, आँकड़े उतने ही अधिक फैले हुए होंगे।

Variance Calculator | प्रसरण कैलकुलेटर – Population & Sample Variance

Variance Calculator

Calculate Population & Sample Variance for Individual, Discrete, Continuous series using Direct & Indirect methods

Individual

Discrete

Continuous

Direct Method

Indirect Method

Population

Sample

Enter values:

Enter individual values as comma-separated list.

How to use the Variance Calculator:

Select series type (Individual, Discrete, or Continuous)
Choose calculation method (Direct or Indirect)
Select data type (Population or Sample)
Enter values according to the selected series type
For Indirect method, you can enter assumed mean (optional)
Click “Calculate Variance” to see results and step-by-step solution
Click “Download PDF” to save your calculation report
Formula used: Population Variance = Σ(xᵢ-μ)²/N, Sample Variance = Σ(xᵢ-x̄)²/(n-1)

Variance Calculation Results

Mean (माध्य)

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Sum of Squares (वर्गों का योग)

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Variance (प्रसरण)

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Calculation Table

Step-by-Step Calculation

Enter your data and click “Calculate Variance”

Variance Calculator

प्रसरण कैलकुलेटर

How to use the Variance Calculator:

प्रसरण कैलकुलेटर का उपयोग कैसे करें:

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