Pooled Variance Calculator

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Measures of Dispersion Basic Formulas in Statistics Coefficients, Proportion and Regression Errors, Sum of Squares, Degrees of Freedom and Hypothesis Testing More >>

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Variance Quartile Deviation Standard Deviation

✖Size of Sample X is the number of observations or data points in Sample X.ⓘ Size of Sample X [N_X]			+10% -10%
✖Variance of Sample X is the average of the squared differences between each data point and the mean of Sample X.ⓘ Variance of Sample X [σ²X]			+10% -10%
✖Size of Sample Y is the number of observations or data points in Sample Y.ⓘ Size of Sample Y [N_Y]			+10% -10%
✖Variance of Sample Y is the average of the squared differences between each data point and the mean of Sample Y.ⓘ Variance of Sample Y [σ²Y]			+10% -10%

✖Pooled Variance is the variance calculated from a combined or pooled dataset, frequently utilized in statistical tests involving multiple groups with comparable features.ⓘ Pooled Variance [V_Pooled]

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Pooled Variance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Pooled Variance = (((Size of Sample X-1)*Variance of Sample X)+((Size of Sample Y-1)*Variance of Sample Y))/(Size of Sample X+Size of Sample Y-2)
V_Pooled = (((N_X-1)*σ²X)+((N_Y-1)*σ²Y))/(N_X+N_Y-2)
This formula uses 5 Variables

Variables Used

Pooled Variance - Pooled Variance is the variance calculated from a combined or pooled dataset, frequently utilized in statistical tests involving multiple groups with comparable features.
Size of Sample X - Size of Sample X is the number of observations or data points in Sample X.
Variance of Sample X - Variance of Sample X is the average of the squared differences between each data point and the mean of Sample X.
Size of Sample Y - Size of Sample Y is the number of observations or data points in Sample Y.
Variance of Sample Y - Variance of Sample Y is the average of the squared differences between each data point and the mean of Sample Y.

STEP 1: Convert Input(s) to Base Unit

Size of Sample X: 8 --> No Conversion Required
Variance of Sample X: 840 --> No Conversion Required
Size of Sample Y: 6 --> No Conversion Required
Variance of Sample Y: 1765 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_Pooled = (((N_X-1)*σ²X)+((N_Y-1)*σ²Y))/(N_X+N_Y-2) --> (((8-1)*840)+((6-1)*1765))/(8+6-2)

Evaluating ... ...

V_Pooled = 1225.41666666667

STEP 3: Convert Result to Output's Unit

1225.41666666667 --> No Conversion Required

FINAL ANSWER

1225.41666666667 ≈ 1225.417 <-- Pooled Variance

(Calculation completed in 00.005 seconds)

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< Variance Calculators

Variance of Data

LaTeX Go Variance of Data = (Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2)

Variance of Sum of Independent Random Variables

LaTeX Go Variance of Sum of Independent Random Variables = Variance of Random Variable X+Variance of Random Variable Y

Variance of Scalar Multiple of Random Variable

LaTeX Go Variance of Scalar Multiple of Random Variable = (Scalar Value c^2)*Variance of Random Variable X

Variance given Standard Deviation

LaTeX Go Variance of Data = (Standard Deviation of Data)^2

Pooled Variance Formula

LaTeX Go

What is Variance and the importance of Variance in Statistics?

Variance is a statistical tool used to analyze a statistical data. The word Variance is actually derived from the word variety that in terms of statistics means the difference among various scores and readings. Basically it is the expectation of the squared deviation of the associated random variable from its population mean or sample mean. Variance ensures accuracy as more Variance is considered good as compared to the low Variance or absolutely absence of any Variance. Variance in statistics is important as in a measurement it allows us to measure the dispersion of the set of the variables around their mean. These set of the variables are the variables that are being measured or analyzed. The presence of the Variance allows a statistician to draw some meaningful conclusion from the data. The advantage of Variance is that it treats all deviations from the mean as the same regardless of their direction.

How to Calculate Pooled Variance?

Pooled Variance calculator uses Pooled Variance = (((Size of Sample X-1)*Variance of Sample X)+((Size of Sample Y-1)*Variance of Sample Y))/(Size of Sample X+Size of Sample Y-2) to calculate the Pooled Variance, Pooled Variance formula is defined as the variance calculated from a combined or pooled dataset, frequently utilized in statistical tests involving multiple groups with comparable features. Pooled Variance is denoted by V_Pooled symbol.

How to calculate Pooled Variance using this online calculator? To use this online calculator for Pooled Variance, enter Size of Sample X (N_X), Variance of Sample X (σ²X), Size of Sample Y (N_Y) & Variance of Sample Y (σ²Y) and hit the calculate button. Here is how the Pooled Variance calculation can be explained with given input values -> 656.6667 = (((8-1)*840)+((6-1)*1765))/(8+6-2).

FAQ

What is Pooled Variance?

Pooled Variance formula is defined as the variance calculated from a combined or pooled dataset, frequently utilized in statistical tests involving multiple groups with comparable features and is represented as V_Pooled = (((N_X-1)*σ²X)+((N_Y-1)*σ²Y))/(N_X+N_Y-2) or Pooled Variance = (((Size of Sample X-1)*Variance of Sample X)+((Size of Sample Y-1)*Variance of Sample Y))/(Size of Sample X+Size of Sample Y-2). Size of Sample X is the number of observations or data points in Sample X, Variance of Sample X is the average of the squared differences between each data point and the mean of Sample X, Size of Sample Y is the number of observations or data points in Sample Y & Variance of Sample Y is the average of the squared differences between each data point and the mean of Sample Y.

How to calculate Pooled Variance?

Pooled Variance formula is defined as the variance calculated from a combined or pooled dataset, frequently utilized in statistical tests involving multiple groups with comparable features is calculated using Pooled Variance = (((Size of Sample X-1)*Variance of Sample X)+((Size of Sample Y-1)*Variance of Sample Y))/(Size of Sample X+Size of Sample Y-2). To calculate Pooled Variance, you need Size of Sample X (N_X), Variance of Sample X (σ²X), Size of Sample Y (N_Y) & Variance of Sample Y (σ²Y). With our tool, you need to enter the respective value for Size of Sample X, Variance of Sample X, Size of Sample Y & Variance of Sample Y 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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