Observed Value given Residual Error Calculator

✖Residual error is the difference between the most probable value of a quantity and its observed value.ⓘ Residual Error [r]			+10% -10%
✖Most probable value of a quantity is the one which has more chances of being true than has any other. It is deduced from the several measurements on which it is based.ⓘ Most Probable Value [MPV]			+10% -10%

✖Observed value is the value which the observer notes during surveying.ⓘ Observed Value given Residual Error [x]

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Formula

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Observed Value given Residual Error

Formula

`"x" = "r"+"MPV"`

Example

`"159"="80"+"79"`

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Observed Value given Residual Error Solution

STEP 0: Pre-Calculation Summary

Formula Used

Observed Value = Residual Error+Most Probable Value
x = r+MPV
This formula uses 3 Variables

Variables Used

Observed Value - Observed value is the value which the observer notes during surveying.
Residual Error - Residual error is the difference between the most probable value of a quantity and its observed value.
Most Probable Value - Most probable value of a quantity is the one which has more chances of being true than has any other. It is deduced from the several measurements on which it is based.

STEP 1: Convert Input(s) to Base Unit

Residual Error: 80 --> No Conversion Required
Most Probable Value: 79 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x = r+MPV --> 80+79

Evaluating ... ...

x = 159

STEP 3: Convert Result to Output's Unit

159 --> No Conversion Required

FINAL ANSWER

159 <-- Observed Value

(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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< 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

Observed Value given Residual Error Formula

Observed Value = Residual Error+Most Probable Value
x = r+MPV

What are different types of Errors?

Errors of measurement are of three kinds:
(i) Mistakes: Mistakes are errors that arise from inattention, inexperience, carelessness and poor judgment or confusion in the mind of the observer.
(ii) Systematic errors: A systematic error is an error that under the same conditions will always be of the same size and sign.
(iii) Accidental errors: Accidental errors are those which remain after mistakes and systematic errors have been eliminated and are caused by a combination of reasons beyond the ability of the observer to control.

How to Calculate Observed Value given Residual Error?

Observed Value given Residual Error calculator uses Observed Value = Residual Error+Most Probable Value to calculate the Observed Value, The Observed Value given Residual Error formula is defined as the residual error and most probable value in a surveying process. For a finite number of measurements, the residual r is approximately equal to the true error ε. Observed Value is denoted by x symbol.

How to calculate Observed Value given Residual Error using this online calculator? To use this online calculator for Observed Value given Residual Error, enter Residual Error (r) & Most Probable Value (MPV) and hit the calculate button. Here is how the Observed Value given Residual Error calculation can be explained with given input values -> 159 = 80+79.

FAQ

What is Observed Value given Residual Error?

The Observed Value given Residual Error formula is defined as the residual error and most probable value in a surveying process. For a finite number of measurements, the residual r is approximately equal to the true error ε and is represented as x = r+MPV or Observed Value = Residual Error+Most Probable Value. Residual error is the difference between the most probable value of a quantity and its observed value & Most probable value of a quantity is the one which has more chances of being true than has any other. It is deduced from the several measurements on which it is based.

How to calculate Observed Value given Residual Error?

The Observed Value given Residual Error formula is defined as the residual error and most probable value in a surveying process. For a finite number of measurements, the residual r is approximately equal to the true error ε is calculated using Observed Value = Residual Error+Most Probable Value. To calculate Observed Value given Residual Error, you need Residual Error (r) & Most Probable Value (MPV). With our tool, you need to enter the respective value for Residual Error & Most Probable Value and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Observed Value?

In this formula, Observed Value uses Residual Error & Most Probable Value. We can use 2 other way(s) to calculate the same, which is/are as follows -

Observed Value = True Value-True Error
Observed Value = True Error/Relative Error

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