Observed Value given Relative Error Calculator

✖True error is the difference between the true value of a quantity and its observed value.ⓘ True Error [ε_x]			+10% -10%
✖Relative error is a measure of the error in relation to the size of the measurement.ⓘ Relative Error [R_x]			+10% -10%

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

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Formula

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Observed Value given Relative Error

Formula

`"x" = "ε"_{"x"}/"R"_{"x"}`

Example

`"160"="320"/"2"`

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Observed Value given Relative Error Solution

STEP 0: Pre-Calculation Summary

Formula Used

Observed Value = True Error/Relative Error
x = ε_x/R_x
This formula uses 3 Variables

Variables Used

Observed Value - Observed value is the value which the observer notes during surveying.
True Error - True error is the difference between the true value of a quantity and its observed value.
Relative Error - Relative error is a measure of the error in relation to the size of the measurement.

STEP 1: Convert Input(s) to Base Unit

True Error: 320 --> No Conversion Required
Relative Error: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x = ε_x/R_x --> 320/2

Evaluating ... ...

x = 160

STEP 3: Convert Result to Output's Unit

160 --> No Conversion Required

FINAL ANSWER

160 <-- Observed Value

(Calculation completed in 00.004 seconds)

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NSS College of Engineering (NSSCE), Palakkad

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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 Relative Error Formula

Observed Value = True Error/Relative Error
x = ε_x/R_x

How an Observed Quantity can be Classified?

An observed quantity may be classified as (i) independent and (ii) conditioned.
(i) independent: An independent quantity is the one whose value is independent of the values of other
quantities.
(ii) conditioned: A conditioned quantity is the one whose value is dependent upon the values of
one or more quantities.

How to Calculate Observed Value given Relative Error?

Observed Value given Relative Error calculator uses Observed Value = True Error/Relative Error to calculate the Observed Value, The Observed Value given Relative Error formula is defined as the ratio of true error to the relative error. Observation is the numerical value of a measured quantity and may be either direct or indirect. Observed Value is denoted by x symbol.

How to calculate Observed Value given Relative Error using this online calculator? To use this online calculator for Observed Value given Relative Error, enter True Error (ε_x) & Relative Error (R_x) and hit the calculate button. Here is how the Observed Value given Relative Error calculation can be explained with given input values -> 160 = 320/2.

FAQ

What is Observed Value given Relative Error?

The Observed Value given Relative Error formula is defined as the ratio of true error to the relative error. Observation is the numerical value of a measured quantity and may be either direct or indirect and is represented as x = ε_x/R_x or Observed Value = True Error/Relative Error. True error is the difference between the true value of a quantity and its observed value & Relative error is a measure of the error in relation to the size of the measurement.

How to calculate Observed Value given Relative Error?

The Observed Value given Relative Error formula is defined as the ratio of true error to the relative error. Observation is the numerical value of a measured quantity and may be either direct or indirect is calculated using Observed Value = True Error/Relative Error. To calculate Observed Value given Relative Error, you need True Error (ε_x) & Relative Error (R_x). With our tool, you need to enter the respective value for True Error & Relative Error 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 True Error & Relative Error. We can use 2 other way(s) to calculate the same, which is/are as follows -

Observed Value = True Value-True Error
Observed Value = Residual Error+Most Probable Value

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