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Standard Deviation of Weighted Observations Formula

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Weighted standard deviation is the standard deviation found when the observations taken are having different weightages. Check FAQs

σ w = \sqrt{\frac{ƩWV 2}{n obs - 1}}

σ_w - Weighted Standard Deviation?ƩWV² - Sum of Weighted Residual Variation?n_obs - Number of Observations?

Standard Deviation of Weighted Observations Example

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Here is how the Standard Deviation of Weighted Observations equation looks like with Values.

Here is how the Standard Deviation of Weighted Observations equation looks like with Units.

Here is how the Standard Deviation of Weighted Observations equation looks like.

22.3607 = \sqrt{\frac{1500}{4 - 1}}

22.3607 = \sqrt{\frac{1500}{4 - 1}}

22.3607 = \sqrt{\frac{1500}{4 - 1}}

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Standard Deviation of Weighted Observations Solution

Follow our step by step solution on how to calculate Standard Deviation of Weighted Observations?

FIRST Step Consider the formula

σ w = \sqrt{\frac{ƩWV 2}{n obs - 1}}

Next Step Substitute values of Variables

∴

σ w = \sqrt{\frac{1500}{4 - 1}}

Next Step Prepare to Evaluate

∴

σ w = \sqrt{\frac{1500}{4 - 1}}

Next Step Evaluate

∴

σ w = 22.3606797749979

LAST Step Rounding Answer

∴

σ w = 22.3607

Standard Deviation of Weighted Observations Formula Elements

Variables

Functions

Weighted Standard Deviation

Weighted standard deviation is the standard deviation found when the observations taken are having different weightages.

Symbol: σ_w

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Weighted Standard Deviation

Sum of Weighted Residual Variation

Sum of Weighted Residual Variation is the addition of the product of squared residual variation and weightage.

Symbol: ƩWV²

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Sum of Weighted Residual Variation

Number of Observations

Number of Observations refers to the number of observations taken in the given data collection.

Symbol: n_obs

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of Observations

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 Theory of Errors category

Go Probable Error of Mean

PE m = \frac{PE s}{{n obs}^{0.5}}

Go Mean Error given Sum of Errors

E m = \frac{ΣE}{n obs}

Go Mean Error given Specified Error of Single Measurement

E m = \frac{E s}{\sqrt{n obs}}

Go True Error

ε x = X - x

How to Evaluate Standard Deviation of Weighted Observations?

Standard Deviation of Weighted Observations evaluator uses Weighted Standard Deviation = sqrt(Sum of Weighted Residual Variation/(Number of Observations-1)) to evaluate the Weighted Standard Deviation, The Standard Deviation of Weighted Observations are the value used for indicating the precision of weighted observed values about a central value. Weighted Standard Deviation is denoted by σ_w symbol.

How to evaluate Standard Deviation of Weighted Observations using this online evaluator? To use this online evaluator for Standard Deviation of Weighted Observations, enter Sum of Weighted Residual Variation (ƩWV²) & Number of Observations (n_obs) and hit the calculate button.

FAQs on Standard Deviation of Weighted Observations

What is the formula to find Standard Deviation of Weighted Observations?

The formula of Standard Deviation of Weighted Observations is expressed as Weighted Standard Deviation = sqrt(Sum of Weighted Residual Variation/(Number of Observations-1)). Here is an example- 22.36068 = sqrt(1500/(4-1)).

How to calculate Standard Deviation of Weighted Observations?

With Sum of Weighted Residual Variation (ƩWV²) & Number of Observations (n_obs) we can find Standard Deviation of Weighted Observations using the formula - Weighted Standard Deviation = sqrt(Sum of Weighted Residual Variation/(Number of Observations-1)). This formula also uses Square Root (sqrt) function(s).

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Standard Deviation of Weighted Observations Formula

Standard Deviation of Weighted Observations Example

Standard Deviation of Weighted Observations Solution

Standard Deviation of Weighted Observations Formula Elements

Other formulas in Theory of Errors category

How to Evaluate Standard Deviation of Weighted Observations?

FAQs on Standard Deviation of Weighted Observations

Variable Name