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Pooled Standard Deviation Formula

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Pooled Standard Deviation is the standard deviation calculated from a combined or pooled dataset, often used in the analysis of groups with similar characteristics. Check FAQs

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

σ_Pooled - Pooled Standard Deviation?N_X - Size of Sample X?σ_X - Standard Deviation of Sample X?N_Y - Size of Sample Y?σ_Y - Standard Deviation of Sample Y?

Pooled Standard Deviation Example

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Here is how the Pooled Standard Deviation equation looks like with Values.

Here is how the Pooled Standard Deviation equation looks like with Units.

Here is how the Pooled Standard Deviation equation looks like.

35.0083 = \sqrt{\frac{((8 - 1) \cdot (29^{2})) + ((6 - 1) \cdot (42^{2}))}{8 + 6 - 2}}

35.0083 = \sqrt{\frac{((8 - 1) \cdot (29^{2})) + ((6 - 1) \cdot (42^{2}))}{8 + 6 - 2}}

35.0083 = \sqrt{\frac{((8 - 1) \cdot (29^{2})) + ((6 - 1) \cdot (42^{2}))}{8 + 6 - 2}}

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Pooled Standard Deviation Solution

Follow our step by step solution on how to calculate Pooled Standard Deviation?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ Pooled = \sqrt{\frac{((8 - 1) \cdot (29^{2})) + ((6 - 1) \cdot (42^{2}))}{8 + 6 - 2}}

Next Step Prepare to Evaluate

∴

σ Pooled = \sqrt{\frac{((8 - 1) \cdot (29^{2})) + ((6 - 1) \cdot (42^{2}))}{8 + 6 - 2}}

Next Step Evaluate

∴

σ Pooled = 35.008332341506

LAST Step Rounding Answer

∴

σ Pooled = 35.0083

Pooled Standard Deviation Formula Elements

Variables

Functions

Pooled Standard Deviation

Pooled Standard Deviation is the standard deviation calculated from a combined or pooled dataset, often used in the analysis of groups with similar characteristics.

Symbol: σ_Pooled

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Pooled Standard Deviation

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

Standard Deviation of Sample X

Standard Deviation of Sample X is the measure of how much the values in Sample X vary.

Symbol: σ_X

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Standard Deviation 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

Standard Deviation of Sample Y

Standard Deviation of Sample Y is the measure of how much the values in Sample Y vary.

Symbol: σ_Y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Standard Deviation of Sample Y

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.

Syntax: sqrt(Number)

Other formulas in Standard Deviation category

Go Standard Deviation given Variance

σ = \sqrt{σ 2}

Go Standard Deviation of Sum of Independent Random Variables

σ (X+Y) = \sqrt{({σ X(Random)}^{2}) + ({σ Y(Random)}^{2})}

Go Standard Deviation given Coefficient of Variation Percentage

σ = \frac{μ \cdot CV %}{100}

Go Standard Deviation given Mean

σ = \sqrt{(\frac{Σx 2}{N}) - (μ^{2})}

How to Evaluate Pooled Standard Deviation?

Pooled Standard Deviation evaluator uses Pooled Standard Deviation = sqrt((((Size of Sample X-1)*(Standard Deviation of Sample X^2))+((Size of Sample Y-1)*(Standard Deviation of Sample Y^2)))/(Size of Sample X+Size of Sample Y-2)) to evaluate the Pooled Standard Deviation, Pooled Standard Deviation formula is defined as the standard deviation calculated from a combined or pooled dataset, often used in the analysis of groups with similar characteristics. Pooled Standard Deviation is denoted by σ_Pooled symbol.

How to evaluate Pooled Standard Deviation using this online evaluator? To use this online evaluator for Pooled Standard Deviation, enter Size of Sample X (N_X), Standard Deviation of Sample X (σ_X), Size of Sample Y (N_Y) & Standard Deviation of Sample Y (σ_Y) and hit the calculate button.

FAQs on Pooled Standard Deviation

What is the formula to find Pooled Standard Deviation?

The formula of Pooled Standard Deviation is expressed as Pooled Standard Deviation = sqrt((((Size of Sample X-1)*(Standard Deviation of Sample X^2))+((Size of Sample Y-1)*(Standard Deviation of Sample Y^2)))/(Size of Sample X+Size of Sample Y-2)). Here is an example- 25.63689 = sqrt((((8-1)*(29^2))+((6-1)*(42^2)))/(8+6-2)).

How to calculate Pooled Standard Deviation?

With Size of Sample X (N_X), Standard Deviation of Sample X (σ_X), Size of Sample Y (N_Y) & Standard Deviation of Sample Y (σ_Y) we can find Pooled Standard Deviation using the formula - Pooled Standard Deviation = sqrt((((Size of Sample X-1)*(Standard Deviation of Sample X^2))+((Size of Sample Y-1)*(Standard Deviation of Sample Y^2)))/(Size of Sample X+Size of Sample Y-2)). This formula also uses Square Root (sqrt) function(s).

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Pooled Standard Deviation Formula

Pooled Standard Deviation Example

Pooled Standard Deviation Solution

Pooled Standard Deviation Formula Elements

Other formulas in Standard Deviation category

How to Evaluate Pooled Standard Deviation?

FAQs on Pooled Standard Deviation

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