Variance of Binomial Distribution Calculator

✖Number of Trials is the total number of repetitions of a particular random experiment, under similar circumstances.ⓘ Number of Trials [N_Trials]			+10% -10%
✖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%

✖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 of Binomial Distribution [σ²]

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Variance of Binomial Distribution

Formula

`"σ"^{"2"} = "N"_{"Trials"}*"p"*"q"_{"BD"}`

Example

`"2.4"="10"*"0.6"*"0.4"`

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Variance of Binomial Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Variance of Data = Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution
σ² = N_Trials*p*q_BD
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.
Number of Trials - Number of Trials is the total number of repetitions of a particular random experiment, under similar circumstances.
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.

STEP 1: Convert Input(s) to Base Unit

Number of Trials: 10 --> No Conversion Required
Probability of Success: 0.6 --> No Conversion Required
Probability of Failure in Binomial Distribution: 0.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ² = N_Trials*p*q_BD --> 10*0.6*0.4

Evaluating ... ...

σ² = 2.4

STEP 3: Convert Result to Output's Unit

2.4 --> No Conversion Required

FINAL ANSWER

2.4 <-- Variance of Data

(Calculation completed in 00.004 seconds)

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Home » Math » Probability and Disribution » Distribution » Binomial Distribution » Variance of Binomial Distribution

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< 8 Binomial Distribution Calculators

Binomial Probability Distribution

Go Binomial Probability = (C(Total Number of Trials,Number of Successful Trials))*Probability of Success in Binomial Distribution^Number of Successful Trials*Probability of Failure^(Total Number of Trials-Number of Successful Trials)

Standard Deviation of Negative Binomial Distribution

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

Standard Deviation of Binomial Distribution

Go Standard Deviation in Normal Distribution = sqrt(Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution)

Mean of Negative Binomial Distribution

Go Mean in Normal Distribution = (Number of Success*Probability of Failure in Binomial Distribution)/Probability of Success

Variance of Negative Binomial Distribution

Go Variance of Data = (Number of Success*Probability of Failure in Binomial Distribution)/(Probability of Success^2)

Variance of Binomial Distribution

Go Variance of Data = Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution

Variance in Binomial Distribution

Go Variance of Data = Number of Trials*Probability of Success*(1-Probability of Success)

Mean of Binomial Distribution

Go Mean in Normal Distribution = Number of Trials*Probability of Success

Variance of Binomial Distribution Formula

Variance of Data = Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution
σ² = N_Trials*p*q_BD

What is Binomial Distribution?

A Binomial Distribution is a probability distribution that describes the number of successful outcomes in a fixed number of independent trials. Each trial has only two possible outcomes, typically labeled "success" and "failure".
The Binomial Distribution is defined by two parameters: the probability of success (p) in a single trial, and the number of trials (n).
The probability of getting exactly k successful outcomes in n trials is given by the binomial probability formula. P(x) = (n choose x) * (p^x) * ((1-p)^(n-x))

It is also a discrete probability distribution, and is used to model the number of successes in a fixed number of Bernoulli trials with a fixed probability of success.

How to Calculate Variance of Binomial Distribution?

Variance of Binomial Distribution calculator uses Variance of Data = Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution to calculate the Variance of Data, Variance of Binomial Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Binomial distribution, from its mean. Variance of Data is denoted by σ² symbol.

How to calculate Variance of Binomial Distribution using this online calculator? To use this online calculator for Variance of Binomial Distribution, enter Number of Trials (N_Trials), Probability of Success (p) & Probability of Failure in Binomial Distribution (q_BD) and hit the calculate button. Here is how the Variance of Binomial Distribution calculation can be explained with given input values -> 2.4 = 10*0.6*0.4.

FAQ

What is Variance of Binomial Distribution?

Variance of Binomial Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Binomial distribution, from its mean and is represented as σ² = N_Trials*p*q_BD or Variance of Data = Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution. Number of Trials is the total number of repetitions of a particular random experiment, under similar circumstances, 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.

How to calculate Variance of Binomial Distribution?

Variance of Binomial Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Binomial distribution, from its mean is calculated using Variance of Data = Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution. To calculate Variance of Binomial Distribution, you need Number of Trials (N_Trials), Probability of Success (p) & Probability of Failure in Binomial Distribution (q_BD). With our tool, you need to enter the respective value for Number of Trials, Probability of Success & Probability of Failure in Binomial Distribution 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 Number of Trials, Probability of Success & Probability of Failure in Binomial Distribution. We can use 2 other way(s) to calculate the same, which is/are as follows -

Variance of Data = (Number of Success*Probability of Failure in Binomial Distribution)/(Probability of Success^2)
Variance of Data = Number of Trials*Probability of Success*(1-Probability of Success)

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