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Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure Calculator

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✖Probability of Success is the probability of a specific outcome occurring in a single trial of a fixed number of independent Bernoulli trials.ⓘ Probability of Success [p]			+10% -10%
✖Probability of Failure in Binomial Distribution is the probability of a specific outcome not occurring in a single trial of a fixed number of independent Bernoulli trials.ⓘ Probability of Failure in Binomial Distribution [q_BD]			+10% -10%
✖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%

✖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.ⓘ Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure [σ²]

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Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure Solution

STEP 0: Pre-Calculation Summary

Formula Used

Variance of Data = (Probability of Success*Probability of Failure in Binomial Distribution)/Sample Size
σ² = (p*q_BD)/n
This formula uses 4 Variables

Variables Used

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.
Probability of Success - Probability of Success is the probability of a specific outcome occurring in a single trial of a fixed number of independent Bernoulli trials.
Probability of Failure in Binomial Distribution - Probability of Failure in Binomial Distribution is the probability of a specific outcome not occurring in a single trial of a fixed number of independent Bernoulli trials.
Sample Size - Sample Size is the total number of individuals present in a particular sample drawn from the given population under investigation.

STEP 1: Convert Input(s) to Base Unit

Probability of Success: 0.6 --> No Conversion Required
Probability of Failure in Binomial Distribution: 0.4 --> No Conversion Required
Sample Size: 65 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ² = (p*q_BD)/n --> (0.6*0.4)/65

Evaluating ... ...

σ² = 0.00369230769230769

STEP 3: Convert Result to Output's Unit

0.00369230769230769 --> No Conversion Required

FINAL ANSWER

0.00369230769230769 ≈ 0.003692 <-- Variance of Data

(Calculation completed in 00.005 seconds)

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< Sampling Distribution Calculators

Standard Deviation of Population in Sampling Distribution of Proportion

LaTeX Go Standard Deviation in Normal Distribution = sqrt((Sum of Squares of Individual Values/Population Size)-((Sum of Individual Values/Population Size)^2))

Standard Deviation in Sampling Distribution of Proportion given Probabilities of Success and Failure

LaTeX Go Standard Deviation in Normal Distribution = sqrt((Probability of Success*Probability of Failure in Binomial Distribution)/Sample Size)

Standard Deviation in Sampling Distribution of Proportion

LaTeX Go Standard Deviation in Normal Distribution = sqrt((Probability of Success*(1-Probability of Success))/Sample Size)

Variance in Sampling Distribution of Proportion

LaTeX Go Variance of Data = (Probability of Success*(1-Probability of Success))/Sample Size

Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure Formula

LaTeX Go

Variance of Data = (Probability of Success*Probability of Failure in Binomial Distribution)/Sample Size
σ² = (p*q_BD)/n

What is Sampling Distribution?

The Sampling Distribution is the probability distribution of a statistic calculated from a random sample drawn from a population. It describes how the value of the statistic is likely to vary across different samples of the same size and shape, drawn from the same population. It is an important concept in statistics because it allows us to make inferences about a population based on sample data. For example, by understanding the sampling distribution of the mean, we can estimate the mean of a population based on the mean of a sample, and calculate the probability that the estimate is close to the true population mean.

How to Calculate Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure?

Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure calculator uses Variance of Data = (Probability of Success*Probability of Failure in Binomial Distribution)/Sample Size to calculate the Variance of Data, Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure formula is defined as the expectation of the squared deviation of the random variable that follows sampling distribution of proportion, from its mean, and calculated using both success and failure probabilities. Variance of Data is denoted by σ² symbol.

How to calculate Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure using this online calculator? To use this online calculator for Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure, enter Probability of Success (p), Probability of Failure in Binomial Distribution (q_BD) & Sample Size (n) and hit the calculate button. Here is how the Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure calculation can be explained with given input values -> 0.003692 = (0.6*0.4)/65.

FAQ

What is Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure?

Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure formula is defined as the expectation of the squared deviation of the random variable that follows sampling distribution of proportion, from its mean, and calculated using both success and failure probabilities and is represented as σ² = (p*q_BD)/n or Variance of Data = (Probability of Success*Probability of Failure in Binomial Distribution)/Sample Size. Probability of Success is the probability of a specific outcome occurring in a single trial of a fixed number of independent Bernoulli trials, Probability of Failure in Binomial Distribution is the probability of a specific outcome not occurring in a single trial of a fixed number of independent Bernoulli trials & Sample Size is the total number of individuals present in a particular sample drawn from the given population under investigation.

How to calculate Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure?

Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure formula is defined as the expectation of the squared deviation of the random variable that follows sampling distribution of proportion, from its mean, and calculated using both success and failure probabilities is calculated using Variance of Data = (Probability of Success*Probability of Failure in Binomial Distribution)/Sample Size. To calculate Variance in Sampling Distribution of Proportion given Probabilities of Success and Failure, you need Probability of Success (p), Probability of Failure in Binomial Distribution (q_BD) & Sample Size (n). With our tool, you need to enter the respective value for Probability of Success, Probability of Failure in Binomial Distribution & Sample Size and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Variance of Data?

In this formula, Variance of Data uses Probability of Success, Probability of Failure in Binomial Distribution & Sample Size. We can use 1 other way(s) to calculate the same, which is/are as follows -

Variance of Data = (Probability of Success*(1-Probability of Success))/Sample Size

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