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)
VPooled = (((NX-1)*σ2X)+((NY-1)*σ2Y))/(NX+NY-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
VPooled = (((NX-1)*σ2X)+((NY-1)*σ2Y))/(NX+NY-2) --> (((8-1)*840)+((6-1)*1765))/(8+6-2)
Evaluating ... ...
VPooled = 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 00.004 seconds)

Credits

Created by Nishan Poojary
Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi
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5 Variance Calculators

Pooled Variance
Go 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)
Variance of Data
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
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
Go Variance of Scalar Multiple of Random Variable = (Scalar Value c^2)*Variance of Random Variable X
Variance given Standard Deviation
Go Variance of Data = (Standard Deviation of Data)^2

Pooled Variance 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)
VPooled = (((NX-1)*σ2X)+((NY-1)*σ2Y))/(NX+NY-2)

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 VPooled symbol.

How to calculate Pooled Variance using this online calculator? To use this online calculator for Pooled Variance, enter Size of Sample X (NX), Variance of Sample X 2X), Size of Sample Y (NY) & Variance of Sample Y 2Y) 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 VPooled = (((NX-1)*σ2X)+((NY-1)*σ2Y))/(NX+NY-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 (NX), Variance of Sample X 2X), Size of Sample Y (NY) & Variance of Sample Y 2Y). 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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