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Pooled Variance Formula

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Pooled Variance is the variance calculated from a combined or pooled dataset, frequently utilized in statistical tests involving multiple groups with comparable features. Check FAQs

V Pooled = \frac{((N X - 1) \cdot σ 2 X) + ((N Y - 1) \cdot σ 2 Y)}{N X + N Y - 2}

V_Pooled - Pooled Variance?N_X - Size of Sample X?σ²X - Variance of Sample X?N_Y - Size of Sample Y?σ²Y - Variance of Sample Y?

Pooled Variance Example

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Here is how the Pooled Variance equation looks like with Values.

Here is how the Pooled Variance equation looks like with Units.

Here is how the Pooled Variance equation looks like.

1225.4167 = \frac{((8 - 1) \cdot 840) + ((6 - 1) \cdot 1765)}{8 + 6 - 2}

1225.4167 = \frac{((8 - 1) \cdot 840) + ((6 - 1) \cdot 1765)}{8 + 6 - 2}

1225.4167 = \frac{((8 - 1) \cdot 840) + ((6 - 1) \cdot 1765)}{8 + 6 - 2}

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Pooled Variance Solution

Follow our step by step solution on how to calculate Pooled Variance?

FIRST Step Consider the formula

V Pooled = \frac{((N X - 1) \cdot σ 2 X) + ((N Y - 1) \cdot σ 2 Y)}{N X + N Y - 2}

Next Step Substitute values of Variables

∴

V Pooled = \frac{((8 - 1) \cdot 840) + ((6 - 1) \cdot 1765)}{8 + 6 - 2}

Next Step Prepare to Evaluate

∴

V Pooled = \frac{((8 - 1) \cdot 840) + ((6 - 1) \cdot 1765)}{8 + 6 - 2}

Next Step Evaluate

∴

V Pooled = 1225.41666666667

LAST Step Rounding Answer

∴

V Pooled = 1225.4167

Pooled Variance Formula Elements

Variables

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.

Symbol: V_Pooled

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Pooled Variance

Size of Sample X

Size of Sample X is the number of observations or data points in Sample X.

Symbol: N_X

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Size of 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.

Symbol: σ²X

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Variance of Sample X

Size of Sample Y

Size of Sample Y is the number of observations or data points in Sample Y.

Symbol: N_Y

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Size of 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.

Symbol: σ²Y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Variance of Sample Y

Other formulas in Variance category

Go Variance of Scalar Multiple of Random Variable

V cX = (c^{2}) \cdot σ 2 Random X

Go Variance of Sum of Independent Random Variables

σ 2 Sum = σ 2 Random X + σ 2 Random Y

Go Variance of Data

σ 2 = (\frac{Σx 2}{N}) - (μ^{2})

Go Variance given Standard Deviation

σ 2 = {(σ)}^{2}

How to Evaluate Pooled Variance?

Pooled Variance evaluator 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 evaluate 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 evaluate Pooled Variance using this online evaluator? To use this online evaluator 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.

FAQs on Pooled Variance

What is the formula to find Pooled Variance?

The formula of Pooled Variance is expressed as 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). Here is an example- 656.6667 = (((8-1)*840)+((6-1)*1765))/(8+6-2).

How to calculate Pooled Variance?

With Size of Sample X (N_X), Variance of Sample X (σ²X), Size of Sample Y (N_Y) & Variance of Sample Y (σ²Y) we can find Pooled Variance using the formula - 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).

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Pooled Variance Formula

Pooled Variance Example

Pooled Variance Solution

Pooled Variance Formula Elements

Other formulas in Variance category

How to Evaluate Pooled Variance?

FAQs on Pooled Variance

Variable Name