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]

⎘ Copy

👎

Formula

✖

Standard Deviation of Weighted Observations

Formula

`"σ"_{"w"} = sqrt("ƩWV"^{"2"}/("n"_{"obs"}-1))`

Example

`"22.36068"=sqrt("1500"/("4"-1))`

Calculator

LaTeX

Reset

👍

Download Theory of Errors Formulas PDF

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)

You are here -

Home » Engineering » Civil » Surveying Formulas » Theory of Errors » Standard Deviation of Weighted Observations

Credits

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< 21 Theory of Errors Calculators

Standard Error of Function where variables are Subjected to Addition

Go Standard Error in Function = sqrt(Standard Error in x coordinate^2+Standard Error in y coordinate^2+Standard Error in z coordinate^2)

Most Probable Value with Different Weightage

Go Most Probable Value = add(Weightage*Measured Quantity)/add(Weightage)

Standard Deviation of Weighted Observations

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

Standard Deviation used for Survey Errors

Go Standard Deviation = sqrt(Sum of Square of Residual Variation/(Number of Observations-1))

Mean Error given Specified Error of Single Measurement

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

Standard Error of Mean of Weighted Observations

Go Standard Error of Mean = Weighted Standard Deviation/sqrt(Sum of Weightage)

Probable Error of Mean

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

Variance of Observations

Go Variance = Sum of Square of Residual Variation/(Number of Observations-1)

Mean Error given Sum of Errors

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

Most Probable Value with Same Weightage for Observations

Go Most Probable Value = Sum of Observed Values/Number of Observations

Residual Variation given Most Probable Value

Go Residual Variation = Measured Value-Most Probable Value

Most Probable Value given Residual Error

Go Most Probable Value = Observed Value-Residual Error

Observed Value given Residual Error

Go Observed Value = Residual Error+Most Probable Value

Residual Error

Go Residual Error = Observed Value-Most Probable Value

Observed Value given Relative Error

Go Observed Value = True Error/Relative Error

True Error given Relative Error

Go True Error = Relative Error*Observed Value

Relative Error

Go Relative Error = True Error/Observed Value

Observed Value given True Error

Go Observed Value = True Value-True Error

True Value given True Error

Go True Value = True Error+Observed Value

True Error

Go True Error = True Value-Observed Value

Most Probable Error given Standard Deviation

Go Most Probable Error = 0.6745*Standard Deviation

Standard Deviation of Weighted Observations Formula

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.

Home

FREE PDFs

🔍 Search