Standard Deviation of Weighted Observations Calculator

✖Sum of Weighted Residual Variation is the addition of the product of squared residual variation and weightage.ⓘ Sum of Weighted Residual Variation [ƩWV²]			+10% -10%
✖Number of Observations refers to the number of observations taken in the given data collection.ⓘ Number of Observations [n_obs]			+10% -10%

✖Weighted standard deviation is the standard deviation found when the observations taken are having different weightages.ⓘ Standard Deviation of Weighted Observations [σ_w]

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Standard Deviation of Weighted Observations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Weighted Standard Deviation = sqrt(Sum of Weighted Residual Variation/(Number of Observations-1))
σ_w = sqrt(ƩWV²/(n_obs-1))
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

Weighted Standard Deviation - Weighted standard deviation is the standard deviation found when the observations taken are having different weightages.
Sum of Weighted Residual Variation - Sum of Weighted Residual Variation is the addition of the product of squared residual variation and weightage.
Number of Observations - Number of Observations refers to the number of observations taken in the given data collection.

STEP 1: Convert Input(s) to Base Unit

Sum of Weighted Residual Variation: 1500 --> No Conversion Required
Number of Observations: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_w = sqrt(ƩWV²/(n_obs-1)) --> sqrt(1500/(4-1))

Evaluating ... ...

σ_w = 22.3606797749979

STEP 3: Convert Result to Output's Unit

22.3606797749979 --> No Conversion Required

FINAL ANSWER

22.3606797749979 ≈ 22.36068 <-- Weighted Standard Deviation

(Calculation completed in 00.004 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< Theory of Errors Calculators

Mean Error given Specified Error of Single Measurement

LaTeX Go Error of Mean = Specified Error of a Single Measurement/(sqrt(Number of Observations))

Probable Error of Mean

LaTeX Go Probable Mean of Error = Probable Error in Single Measurement/(Number of Observations^0.5)

Mean Error given Sum of Errors

LaTeX Go Error of Mean = Sum of Errors of Observations/Number of Observations

True Error

LaTeX Go True Error = True Value-Observed Value

Standard Deviation of Weighted Observations Formula

LaTeX Go

Weighted Standard Deviation = sqrt(Sum of Weighted Residual Variation/(Number of Observations-1))
σ_w = sqrt(ƩWV²/(n_obs-1))

What are the Laws of Weightage?

1. The weight of the arithmetic mean of the measurements of unit weight is equal to the number of observations.
2. The weight of the weighted arithmetic mean is equal to the sum of the individual weights.
3. The weight of algebraic sum of two or more quantities is equal to the reciprocals of the individual weights.
4. If a quantity of given weight is multiplied by a factor, the weight of the result is obtained by dividing its given weight by the square of the factor.
5. If a quantity of given weight is divided by a factor, the weight of the result is obtained by multiplying its given weight by the square of the factor.

How to Calculate Standard Deviation of Weighted Observations?

Standard Deviation of Weighted Observations calculator uses Weighted Standard Deviation = sqrt(Sum of Weighted Residual Variation/(Number of Observations-1)) to calculate 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 calculate Standard Deviation of Weighted Observations using this online calculator? To use this online calculator for Standard Deviation of Weighted Observations, enter Sum of Weighted Residual Variation (ƩWV²) & Number of Observations (n_obs) and hit the calculate button. Here is how the Standard Deviation of Weighted Observations calculation can be explained with given input values -> 22.36068 = sqrt(1500/(4-1)).

FAQ

What is Standard Deviation of Weighted Observations?

The Standard Deviation of Weighted Observations are the value used for indicating the precision of weighted observed values about a central value and is represented as σ_w = sqrt(ƩWV²/(n_obs-1)) or Weighted Standard Deviation = sqrt(Sum of Weighted Residual Variation/(Number of Observations-1)). Sum of Weighted Residual Variation is the addition of the product of squared residual variation and weightage & Number of Observations refers to the number of observations taken in the given data collection.

How to calculate Standard Deviation of Weighted Observations?

The Standard Deviation of Weighted Observations are the value used for indicating the precision of weighted observed values about a central value is calculated using Weighted Standard Deviation = sqrt(Sum of Weighted Residual Variation/(Number of Observations-1)). To calculate Standard Deviation of Weighted Observations, you need Sum of Weighted Residual Variation (ƩWV²) & Number of Observations (n_obs). With our tool, you need to enter the respective value for Sum of Weighted Residual Variation & Number of Observations 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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