Pooled Standard Deviation Calculator

✖Size of Sample X is the number of observations or data points in Sample X.ⓘ Size of Sample X [N_X]			+10% -10%
✖Standard Deviation of Sample X is the measure of how much the values in Sample X vary.ⓘ Standard Deviation of Sample X [σ_X]			+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%
✖Standard Deviation of Sample Y is the measure of how much the values in Sample Y vary.ⓘ Standard Deviation of Sample Y [σ_Y]			+10% -10%

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

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Pooled Standard Deviation

Formula

`"σ"_{"Pooled"} = sqrt(((("N"_{"X"}-1)*("σ"_{"X"}^2))+(("N"_{"Y"}-1)*("σ"_{"Y"}^2)))/("N"_{"X"}+"N"_{"Y"}-2))`

Example

`"35.00833"=sqrt(((("8"-1)*(("29")^2))+(("6"-1)*(("42")^2)))/("8"+"6"-2))`

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Pooled Standard Deviation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
σ_Pooled = sqrt((((N_X-1)*(σ_X^2))+((N_Y-1)*(σ_Y^2)))/(N_X+N_Y-2))
This formula uses 1 Functions, 5 Variables

Functions Used

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., sqrt(Number)

Variables Used

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.
Size of Sample X - Size of Sample X is the number of observations or data points in Sample X.
Standard Deviation of Sample X - Standard Deviation of Sample X is the measure of how much the values in Sample X vary.
Size of Sample Y - Size of Sample Y is the number of observations or data points in Sample Y.
Standard Deviation of Sample Y - Standard Deviation of Sample Y is the measure of how much the values in Sample Y vary.

STEP 1: Convert Input(s) to Base Unit

Size of Sample X: 8 --> No Conversion Required
Standard Deviation of Sample X: 29 --> No Conversion Required
Size of Sample Y: 6 --> No Conversion Required
Standard Deviation of Sample Y: 42 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_Pooled = sqrt((((N_X-1)*(σ_X^2))+((N_Y-1)*(σ_Y^2)))/(N_X+N_Y-2)) --> sqrt((((8-1)*(29^2))+((6-1)*(42^2)))/(8+6-2))

Evaluating ... ...

σ_Pooled = 35.008332341506

STEP 3: Convert Result to Output's Unit

35.008332341506 --> No Conversion Required

FINAL ANSWER

35.008332341506 ≈ 35.00833 <-- Pooled Standard Deviation

(Calculation completed in 00.004 seconds)

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< 7 Standard Deviation Calculators

Pooled Standard Deviation

Go 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))

Standard Deviation of Data

Go Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-((Sum of Individual Values/Number of Individual Values)^2))

Standard Deviation given Mean

Go Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2))

Standard Deviation of Sum of Independent Random Variables

Go Standard Deviation of Sum of Random Variables = sqrt((Standard Deviation of Random Variable X^2)+(Standard Deviation of Random Variable Y^2))

Standard Deviation given Coefficient of Variation Percentage

Go Standard Deviation of Data = (Mean of Data*Coefficient of Variation Percentage)/100

Standard Deviation given Coefficient of Variation

Go Standard Deviation of Data = Mean of Data*Coefficient of Variation Ratio

Standard Deviation given Variance

Go Standard Deviation of Data = sqrt(Variance of Data)

Pooled Standard Deviation Formula

What is Standard Deviation in Statistics?

In Statistics, the Standard Deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. The Standard Deviation of a random variable, sample, statistical population, data set, or probability distribution is defined and calculated as the square root of its variance.

How to Calculate Pooled Standard Deviation?

Pooled Standard Deviation calculator 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 calculate 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 calculate Pooled Standard Deviation using this online calculator? To use this online calculator 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. Here is how the Pooled Standard Deviation calculation can be explained with given input values -> 25.63689 = sqrt((((8-1)*(29^2))+((6-1)*(42^2)))/(8+6-2)).

FAQ

What is 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 and is represented as σ_Pooled = sqrt((((N_X-1)*(σ_X^2))+((N_Y-1)*(σ_Y^2)))/(N_X+N_Y-2)) or 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)). Size of Sample X is the number of observations or data points in Sample X, Standard Deviation of Sample X is the measure of how much the values in Sample X vary, Size of Sample Y is the number of observations or data points in Sample Y & Standard Deviation of Sample Y is the measure of how much the values in Sample Y vary.

How to calculate 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 is calculated using 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 calculate Pooled Standard Deviation, you need 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). With our tool, you need to enter the respective value for Size of Sample X, Standard Deviation of Sample X, Size of Sample Y & Standard Deviation 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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