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Variance of Hypergeometric Distribution Formula

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Variance of Data is the expectation of the squared deviation of the random variable associated with the given statistical data from its population mean or sample mean. Check FAQs

σ 2 = \frac{n \cdot N Success \cdot (N - N Success) \cdot (N - n)}{(N^{2}) \cdot (N - 1)}

σ² - Variance of Data?n - Sample Size?N_Success - Number of Success?N - Population Size?

Variance of Hypergeometric Distribution Example

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Here is how the Variance of Hypergeometric Distribution equation looks like with Values.

Here is how the Variance of Hypergeometric Distribution equation looks like with Units.

Here is how the Variance of Hypergeometric Distribution equation looks like.

1.0915 = \frac{65 \cdot 5 \cdot (100 - 5) \cdot (100 - 65)}{(100^{2}) \cdot (100 - 1)}

1.0915 = \frac{65 \cdot 5 \cdot (100 - 5) \cdot (100 - 65)}{(100^{2}) \cdot (100 - 1)}

1.0915 = \frac{65 \cdot 5 \cdot (100 - 5) \cdot (100 - 65)}{(100^{2}) \cdot (100 - 1)}

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Variance of Hypergeometric Distribution Solution

Follow our step by step solution on how to calculate Variance of Hypergeometric Distribution?

FIRST Step Consider the formula

σ 2 = \frac{n \cdot N Success \cdot (N - N Success) \cdot (N - n)}{(N^{2}) \cdot (N - 1)}

Next Step Substitute values of Variables

∴

σ 2 = \frac{65 \cdot 5 \cdot (100 - 5) \cdot (100 - 65)}{(100^{2}) \cdot (100 - 1)}

Next Step Prepare to Evaluate

∴

σ 2 = \frac{65 \cdot 5 \cdot (100 - 5) \cdot (100 - 65)}{(100^{2}) \cdot (100 - 1)}

Next Step Evaluate

∴

σ 2 = 1.0915404040404

LAST Step Rounding Answer

∴

σ 2 = 1.0915

Variance of Hypergeometric Distribution Formula Elements

Variables

Variance of Data

Variance of Data is the expectation of the squared deviation of the random variable associated with the given statistical data from its population mean or sample mean.

Symbol: σ²

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Variance of Data

Sample Size

Sample Size is the total number of individuals present in a particular sample drawn from the given population under investigation.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Sample Size

Number of Success

Number of Success is the number of times that a specific outcome which is set as the success of the event occurs in a fixed number of independent Bernoulli trials.

Symbol: N_Success

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Success

Population Size

Population Size is the total number of individuals present in the given population under investigation.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Population Size

Other formulas in Hypergeometric Distribution category

Go Mean of Hypergeometric Distribution

μ = \frac{n \cdot N Success}{N}

Go Standard Deviation of Hypergeometric Distribution

σ = \sqrt{\frac{n \cdot N Success \cdot (N - N Success) \cdot (N - n)}{(N^{2}) \cdot (N - 1)}}

Go Hypergeometric Distribution

P Hypergeometric = \frac{C (m Sample, x Sample) \cdot C (N Population - m Sample, n Population - x Sample)}{C (N Population, n Population)}

How to Evaluate Variance of Hypergeometric Distribution?

Variance of Hypergeometric Distribution evaluator uses Variance of Data = (Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1)) to evaluate the Variance of Data, Variance of Hypergeometric Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Hypergeometric distribution, from its mean. Variance of Data is denoted by σ² symbol.

How to evaluate Variance of Hypergeometric Distribution using this online evaluator? To use this online evaluator for Variance of Hypergeometric Distribution, enter Sample Size (n), Number of Success (N_Success) & Population Size (N) and hit the calculate button.

FAQs on Variance of Hypergeometric Distribution

What is the formula to find Variance of Hypergeometric Distribution?

The formula of Variance of Hypergeometric Distribution is expressed as Variance of Data = (Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1)). Here is an example- 1.09154 = (65*5*(100-5)*(100-65))/((100^2)*(100-1)).

How to calculate Variance of Hypergeometric Distribution?

With Sample Size (n), Number of Success (N_Success) & Population Size (N) we can find Variance of Hypergeometric Distribution using the formula - Variance of Data = (Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1)).

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Variance of Hypergeometric Distribution Formula

Variance of Hypergeometric Distribution Example

Variance of Hypergeometric Distribution Solution

Variance of Hypergeometric Distribution Formula Elements

Other formulas in Hypergeometric Distribution category

How to Evaluate Variance of Hypergeometric Distribution?

FAQs on Variance of Hypergeometric Distribution

Variable Name