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Standard Deviation of Hypergeometric Distribution Calculator

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✖Sample Size is the total number of individuals present in a particular sample drawn from the given population under investigation.ⓘ Sample Size [n]			+10% -10%
✖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.ⓘ Number of Success [N_Success]			+10% -10%
✖Population Size is the total number of individuals present in the given population under investigation.ⓘ Population Size [N]			+10% -10%

✖Standard Deviation in Normal Distribution is the square root of expectation of the squared deviation of the given normal distribution following data from its population mean or sample mean.ⓘ Standard Deviation of Hypergeometric Distribution [σ]

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Standard Deviation of Hypergeometric Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standard Deviation in Normal Distribution = sqrt((Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1)))
σ = sqrt((n*N_Success*(N-N_Success)*(N-n))/((N^2)*(N-1)))
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Standard Deviation in Normal Distribution - Standard Deviation in Normal Distribution is the square root of expectation of the squared deviation of the given normal distribution following data from its population mean or sample mean.
Sample Size - Sample Size is the total number of individuals present in a particular sample drawn from the given population under investigation.
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.
Population Size - Population Size is the total number of individuals present in the given population under investigation.

STEP 1: Convert Input(s) to Base Unit

Sample Size: 65 --> No Conversion Required
Number of Success: 5 --> No Conversion Required
Population Size: 100 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ = sqrt((n*N_Success*(N-N_Success)*(N-n))/((N^2)*(N-1))) --> sqrt((65*5*(100-5)*(100-65))/((100^2)*(100-1)))

Evaluating ... ...

σ = 1.04476811017584

STEP 3: Convert Result to Output's Unit

1.04476811017584 --> No Conversion Required

FINAL ANSWER

1.04476811017584 ≈ 1.044768 <-- Standard Deviation in Normal Distribution

(Calculation completed in 00.004 seconds)

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< Hypergeometric Distribution Calculators

Hypergeometric Distribution

LaTeX Go Hypergeometric Probability Distribution Function = (C(Number of Items in Sample,Number of Successes in Sample)*C(Number of Items in Population-Number of Items in Sample,Number of Successes in Population-Number of Successes in Sample))/(C(Number of Items in Population,Number of Successes in Population))

Standard Deviation of Hypergeometric Distribution

LaTeX Go Standard Deviation in Normal Distribution = sqrt((Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1)))

Variance of Hypergeometric Distribution

LaTeX Go Variance of Data = (Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1))

Mean of Hypergeometric Distribution

LaTeX Go Mean in Normal Distribution = (Sample Size*Number of Success)/(Population Size)

Standard Deviation of Hypergeometric Distribution Formula

LaTeX Go

What is Hypergeometric Distribution?

The Hypergeometric Distribution is a discrete probability distribution that describes the number of successes in a fixed number of Bernoulli trials (i.e. trials with only two possible outcomes: success or failure) without replacement.
The probability mass function (PMF) of the hypergeometric distribution is given by: P(X = x) = (C(K,x) * C(N-K,n-x)) / C(N,n)

The Hypergeometric Distribution is used to model the probability of observing a certain number of "successes" in a fixed number of draws from a finite population, where the probability of success changes on each draw. It is used in many fields such as genetics, quality control, and sampling inspection, in which the sample is drawn without replacement.

How to Calculate Standard Deviation of Hypergeometric Distribution?

Standard Deviation of Hypergeometric Distribution calculator uses Standard Deviation in Normal Distribution = sqrt((Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1))) to calculate the Standard Deviation in Normal Distribution, Standard Deviation of Hypergeometric Distribution formula is defined as the square root of expectation of the squared deviation of the random variable that follows Hypergeometric distribution, from its mean. Standard Deviation in Normal Distribution is denoted by σ symbol.

How to calculate Standard Deviation of Hypergeometric Distribution using this online calculator? To use this online calculator for Standard Deviation of Hypergeometric Distribution, enter Sample Size (n), Number of Success (N_Success) & Population Size (N) and hit the calculate button. Here is how the Standard Deviation of Hypergeometric Distribution calculation can be explained with given input values -> 1.044768 = sqrt((65*5*(100-5)*(100-65))/((100^2)*(100-1))).

FAQ

What is Standard Deviation of Hypergeometric Distribution?

Standard Deviation of Hypergeometric Distribution formula is defined as the square root of expectation of the squared deviation of the random variable that follows Hypergeometric distribution, from its mean and is represented as σ = sqrt((n*N_Success*(N-N_Success)*(N-n))/((N^2)*(N-1))) or Standard Deviation in Normal Distribution = sqrt((Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1))). Sample Size is the total number of individuals present in a particular sample drawn from the given population under investigation, 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 & Population Size is the total number of individuals present in the given population under investigation.

How to calculate Standard Deviation of Hypergeometric Distribution?

Standard Deviation of Hypergeometric Distribution formula is defined as the square root of expectation of the squared deviation of the random variable that follows Hypergeometric distribution, from its mean is calculated using Standard Deviation in Normal Distribution = sqrt((Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1))). To calculate Standard Deviation of Hypergeometric Distribution, you need Sample Size (n), Number of Success (N_Success) & Population Size (N). With our tool, you need to enter the respective value for Sample Size, Number of Success & Population Size and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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