Standard Error of Mean of Weighted Observations Calculator

✖Weighted standard deviation is the standard deviation found when the observations taken are having different weightages.ⓘ Weighted Standard Deviation [σ_w]			+10% -10%
✖Sum of weightage is the addition of weightage of each observed value if the weight is different for each values.ⓘ Sum of Weightage [ƩW]			+10% -10%

✖Standard error of mean limits the error bound within which the true value of the mean lies.ⓘ Standard Error of Mean of Weighted Observations [σ_nw]

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Formula

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Standard Error of Mean of Weighted Observations

Formula

`"σ"_{"nw"} = "σ"_{"w"}/sqrt("ƩW")`

Example

`"100.1388"="950"/sqrt("90")`

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Standard Error of Mean of Weighted Observations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standard Error of Mean = Weighted Standard Deviation/sqrt(Sum of Weightage)
σ_nw = σ_w/sqrt(ƩW)
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 Error of Mean - Standard error of mean limits the error bound within which the true value of the mean lies.
Weighted Standard Deviation - Weighted standard deviation is the standard deviation found when the observations taken are having different weightages.
Sum of Weightage - Sum of weightage is the addition of weightage of each observed value if the weight is different for each values.

STEP 1: Convert Input(s) to Base Unit

Weighted Standard Deviation: 950 --> No Conversion Required
Sum of Weightage: 90 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_nw = σ_w/sqrt(ƩW) --> 950/sqrt(90)

Evaluating ... ...

σ_nw = 100.138792571999

STEP 3: Convert Result to Output's Unit

100.138792571999 --> No Conversion Required

FINAL ANSWER

100.138792571999 ≈ 100.1388 <-- Standard Error of Mean

(Calculation completed in 00.020 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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< 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 Error of Mean of Weighted Observations Formula

Standard Error of Mean = Weighted Standard Deviation/sqrt(Sum of Weightage)
σ_nw = σ_w/sqrt(ƩW)

What is Distribution of Error of the Field Measurement?

Whenever observations are made in the field, it is always necessary to check for the closing error, if any. The closing error should be distributed to the observed quantities. The following rules should be applied for the distribution of errors:
1) The correction to be applied to an observation is inversely proportional to the weight of the observation.
2) The correction to be applied to an observation is directly proportional to the square of the probable error.
3) In case of line of levels, the correction to be applied is proportional to the length.

How to Calculate Standard Error of Mean of Weighted Observations?

Standard Error of Mean of Weighted Observations calculator uses Standard Error of Mean = Weighted Standard Deviation/sqrt(Sum of Weightage) to calculate the Standard Error of Mean, The Standard Error of Mean of Weighted Observations is the standard deviation of the mean values of weighted observed values. It limits the error bound within which the true value of the mean lies. Standard Error of Mean is denoted by σ_nw symbol.

How to calculate Standard Error of Mean of Weighted Observations using this online calculator? To use this online calculator for Standard Error of Mean of Weighted Observations, enter Weighted Standard Deviation (σ_w) & Sum of Weightage (ƩW) and hit the calculate button. Here is how the Standard Error of Mean of Weighted Observations calculation can be explained with given input values -> 100.1388 = 950/sqrt(90).

FAQ

What is Standard Error of Mean of Weighted Observations?

The Standard Error of Mean of Weighted Observations is the standard deviation of the mean values of weighted observed values. It limits the error bound within which the true value of the mean lies and is represented as σ_nw = σ_w/sqrt(ƩW) or Standard Error of Mean = Weighted Standard Deviation/sqrt(Sum of Weightage). Weighted standard deviation is the standard deviation found when the observations taken are having different weightages & Sum of weightage is the addition of weightage of each observed value if the weight is different for each values.

How to calculate Standard Error of Mean of Weighted Observations?

The Standard Error of Mean of Weighted Observations is the standard deviation of the mean values of weighted observed values. It limits the error bound within which the true value of the mean lies is calculated using Standard Error of Mean = Weighted Standard Deviation/sqrt(Sum of Weightage). To calculate Standard Error of Mean of Weighted Observations, you need Weighted Standard Deviation (σ_w) & Sum of Weightage (ƩW). With our tool, you need to enter the respective value for Weighted Standard Deviation & Sum of Weightage 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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