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))
σPooled = sqrt((((NX-1)*(σX^2))+((NY-1)*(σY^2)))/(NX+NY-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
σPooled = sqrt((((NX-1)*(σX^2))+((NY-1)*(σY^2)))/(NX+NY-2)) --> sqrt((((8-1)*(29^2))+((6-1)*(42^2)))/(8+6-2))
Evaluating ... ...
σPooled = 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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Created by Nishan Poojary
Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi
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Standard Deviation Calculators

Pooled Standard Deviation
​ LaTeX ​ 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 Sum of Independent Random Variables
​ LaTeX ​ 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
​ LaTeX ​ Go Standard Deviation of Data = (Mean of Data*Coefficient of Variation Percentage)/100
Standard Deviation given Variance
​ LaTeX ​ Go Standard Deviation of Data = sqrt(Variance of Data)

Pooled Standard Deviation Formula

​LaTeX ​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))
σPooled = sqrt((((NX-1)*(σX^2))+((NY-1)*(σY^2)))/(NX+NY-2))

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 σPooled 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 (NX), Standard Deviation of Sample X X), Size of Sample Y (NY) & Standard Deviation of Sample Y 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 σPooled = sqrt((((NX-1)*(σX^2))+((NY-1)*(σY^2)))/(NX+NY-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 (NX), Standard Deviation of Sample X X), Size of Sample Y (NY) & Standard Deviation of Sample Y 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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