Standard Error of Function where variables are Subjected to Addition Calculator

✖Standard error in x coordinate is the error obtained in the x coordinate.ⓘ Standard Error in x coordinate [e_x]			+10% -10%
✖Standard error in y coordinate is the error obtained for a quantity in y coordinate.ⓘ Standard Error in y coordinate [e_y]			+10% -10%
✖Standard error in z coordinate is the error obtained in the quantity in z direction.ⓘ Standard Error in z coordinate [e_z]			+10% -10%

✖Standard Error in Function is the error obtained in a quantity as a function.ⓘ Standard Error of Function where variables are Subjected to Addition [e_A]

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Standard Error of Function where variables are Subjected to Addition

Formula

`"e"_{"A"} = sqrt("e"_{"x"}^2+"e"_{"y"}^2+"e"_{"z"}^2)`

Example

`"200.4221"=sqrt(("120")^2+("115")^2+("112")^2)`

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Standard Error of Function where variables are Subjected to Addition Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standard Error in Function = sqrt(Standard Error in x coordinate^2+Standard Error in y coordinate^2+Standard Error in z coordinate^2)
e_A = sqrt(e_x^2+e_y^2+e_z^2)
This formula uses 1 Functions, 4 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 in Function - Standard Error in Function is the error obtained in a quantity as a function.
Standard Error in x coordinate - Standard error in x coordinate is the error obtained in the x coordinate.
Standard Error in y coordinate - Standard error in y coordinate is the error obtained for a quantity in y coordinate.
Standard Error in z coordinate - Standard error in z coordinate is the error obtained in the quantity in z direction.

STEP 1: Convert Input(s) to Base Unit

Standard Error in x coordinate: 120 --> No Conversion Required
Standard Error in y coordinate: 115 --> No Conversion Required
Standard Error in z coordinate: 112 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e_A = sqrt(e_x^2+e_y^2+e_z^2) --> sqrt(120^2+115^2+112^2)

Evaluating ... ...

e_A = 200.422054674629

STEP 3: Convert Result to Output's Unit

200.422054674629 --> No Conversion Required

FINAL ANSWER

200.422054674629 ≈ 200.4221 <-- Standard Error in Function

(Calculation completed in 00.004 seconds)

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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 Function where variables are Subjected to Addition Formula

Standard Error in Function = sqrt(Standard Error in x coordinate^2+Standard Error in y coordinate^2+Standard Error in z coordinate^2)
e_A = sqrt(e_x^2+e_y^2+e_z^2)

What is a Normal Equation?

A normal equation is the one which is formed by multiplying each equation by the coefficient of the unknown whose normal equation is to be found and by adding the equation thus formed.

How to Calculate Standard Error of Function where variables are Subjected to Addition?

Standard Error of Function where variables are Subjected to Addition calculator uses Standard Error in Function = sqrt(Standard Error in x coordinate^2+Standard Error in y coordinate^2+Standard Error in z coordinate^2) to calculate the Standard Error in Function, The Standard Error of Function Where variables are Subjected to Addition is defined when a function of x,y,z need to find the error in the quantity due to errors in x,y,z coordinates. Standard Error in Function is denoted by e_A symbol.

How to calculate Standard Error of Function where variables are Subjected to Addition using this online calculator? To use this online calculator for Standard Error of Function where variables are Subjected to Addition, enter Standard Error in x coordinate (e_x), Standard Error in y coordinate (e_y) & Standard Error in z coordinate (e_z) and hit the calculate button. Here is how the Standard Error of Function where variables are Subjected to Addition calculation can be explained with given input values -> 200.4221 = sqrt(120^2+115^2+112^2).

FAQ

What is Standard Error of Function where variables are Subjected to Addition?

The Standard Error of Function Where variables are Subjected to Addition is defined when a function of x,y,z need to find the error in the quantity due to errors in x,y,z coordinates and is represented as e_A = sqrt(e_x^2+e_y^2+e_z^2) or Standard Error in Function = sqrt(Standard Error in x coordinate^2+Standard Error in y coordinate^2+Standard Error in z coordinate^2). Standard error in x coordinate is the error obtained in the x coordinate, Standard error in y coordinate is the error obtained for a quantity in y coordinate & Standard error in z coordinate is the error obtained in the quantity in z direction.

How to calculate Standard Error of Function where variables are Subjected to Addition?

The Standard Error of Function Where variables are Subjected to Addition is defined when a function of x,y,z need to find the error in the quantity due to errors in x,y,z coordinates is calculated using Standard Error in Function = sqrt(Standard Error in x coordinate^2+Standard Error in y coordinate^2+Standard Error in z coordinate^2). To calculate Standard Error of Function where variables are Subjected to Addition, you need Standard Error in x coordinate (e_x), Standard Error in y coordinate (e_y) & Standard Error in z coordinate (e_z). With our tool, you need to enter the respective value for Standard Error in x coordinate, Standard Error in y coordinate & Standard Error in z coordinate 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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