Standard Deviation of Sum of Independent Random Variables Calculator

✖Standard Deviation of Random Variable X is the measure of variability or dispersion of random variable X.ⓘ Standard Deviation of Random Variable X [σ_X(Random)]			+10% -10%
✖Standard Deviation of Random Variable Y is the measure of variability or dispersion of random variable Y.ⓘ Standard Deviation of Random Variable Y [σ_Y(Random)]			+10% -10%

✖Standard Deviation of Sum of Random Variables is the measure of variability of the sum of two or more independent random variables.ⓘ Standard Deviation of Sum of Independent Random Variables [σ_(X+Y)]

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Standard Deviation of Sum of Independent Random Variables

Formula

`"σ"_{"(X+Y)"} = sqrt(("σ"_{"X(Random)"}^2)+("σ"_{"Y(Random)"}^2))`

Example

`"5"=sqrt((("3")^2)+(("4")^2))`

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Standard Deviation of Sum of Independent Random Variables Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standard Deviation of Sum of Random Variables = sqrt((Standard Deviation of Random Variable X^2)+(Standard Deviation of Random Variable Y^2))
σ_(X+Y) = sqrt((σ_X(Random)^2)+(σ_Y(Random)^2))
This formula uses 1 Functions, 3 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

Standard Deviation of Sum of Random Variables - Standard Deviation of Sum of Random Variables is the measure of variability of the sum of two or more independent random variables.
Standard Deviation of Random Variable X - Standard Deviation of Random Variable X is the measure of variability or dispersion of random variable X.
Standard Deviation of Random Variable Y - Standard Deviation of Random Variable Y is the measure of variability or dispersion of random variable Y.

STEP 1: Convert Input(s) to Base Unit

Standard Deviation of Random Variable X: 3 --> No Conversion Required
Standard Deviation of Random Variable Y: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_(X+Y) = sqrt((σ_X(Random)^2)+(σ_Y(Random)^2)) --> sqrt((3^2)+(4^2))

Evaluating ... ...

σ_(X+Y) = 5

STEP 3: Convert Result to Output's Unit

5 --> No Conversion Required

FINAL ANSWER

5 <-- Standard Deviation of Sum of Random Variables

(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)

Standard Deviation of Sum of Independent Random Variables Formula

Standard Deviation of Sum of Random Variables = sqrt((Standard Deviation of Random Variable X^2)+(Standard Deviation of Random Variable Y^2))
σ_(X+Y) = sqrt((σ_X(Random)^2)+(σ_Y(Random)^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 Standard Deviation of Sum of Independent Random Variables?

Standard Deviation of Sum of Independent Random Variables calculator uses Standard Deviation of Sum of Random Variables = sqrt((Standard Deviation of Random Variable X^2)+(Standard Deviation of Random Variable Y^2)) to calculate the Standard Deviation of Sum of Random Variables, Standard Deviation of Sum of Independent Random Variables formula is defined as the measure of variability of the sum of two or more independent random variables. Standard Deviation of Sum of Random Variables is denoted by σ_(X+Y) symbol.

How to calculate Standard Deviation of Sum of Independent Random Variables using this online calculator? To use this online calculator for Standard Deviation of Sum of Independent Random Variables, enter Standard Deviation of Random Variable X (σ_X(Random)) & Standard Deviation of Random Variable Y (σ_Y(Random)) and hit the calculate button. Here is how the Standard Deviation of Sum of Independent Random Variables calculation can be explained with given input values -> 5 = sqrt((3^2)+(4^2)).

FAQ

What is Standard Deviation of Sum of Independent Random Variables?

Standard Deviation of Sum of Independent Random Variables formula is defined as the measure of variability of the sum of two or more independent random variables and is represented as σ_(X+Y) = sqrt((σ_X(Random)^2)+(σ_Y(Random)^2)) or Standard Deviation of Sum of Random Variables = sqrt((Standard Deviation of Random Variable X^2)+(Standard Deviation of Random Variable Y^2)). Standard Deviation of Random Variable X is the measure of variability or dispersion of random variable X & Standard Deviation of Random Variable Y is the measure of variability or dispersion of random variable Y.

How to calculate Standard Deviation of Sum of Independent Random Variables?

Standard Deviation of Sum of Independent Random Variables formula is defined as the measure of variability of the sum of two or more independent random variables is calculated using Standard Deviation of Sum of Random Variables = sqrt((Standard Deviation of Random Variable X^2)+(Standard Deviation of Random Variable Y^2)). To calculate Standard Deviation of Sum of Independent Random Variables, you need Standard Deviation of Random Variable X (σ_X(Random)) & Standard Deviation of Random Variable Y (σ_Y(Random)). With our tool, you need to enter the respective value for Standard Deviation of Random Variable X & Standard Deviation of Random Variable 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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