Mean Error given Specified Error of Single Measurement Calculator

✖Specified Error of a Single Measurement is error during the separate measurement of quantity.ⓘ Specified Error of a Single Measurement [E_s]			+10% -10%
✖Number of Observations refers to the number of observations taken in the given data collection.ⓘ Number of Observations [n_obs]			+10% -10%

✖Error of Mean is the error in calculating the mean of the observations.ⓘ Mean Error given Specified Error of Single Measurement [E_m]

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Formula

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Mean Error given Specified Error of Single Measurement

Formula

`"E"_{"m"} = "E"_{"s"}/(sqrt("n"_{"obs"}))`

Example

`"0.125"="0.25"/(sqrt("4"))`

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Mean Error given Specified Error of Single Measurement Solution

STEP 0: Pre-Calculation Summary

Formula Used

Error of Mean = Specified Error of a Single Measurement/(sqrt(Number of Observations))
E_m = E_s/(sqrt(n_obs))
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

Error of Mean - Error of Mean is the error in calculating the mean of the observations.
Specified Error of a Single Measurement - Specified Error of a Single Measurement is error during the separate measurement of quantity.
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

Specified Error of a Single Measurement: 0.25 --> No Conversion Required
Number of Observations: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_m = E_s/(sqrt(n_obs)) --> 0.25/(sqrt(4))

Evaluating ... ...

E_m = 0.125

STEP 3: Convert Result to Output's Unit

0.125 --> No Conversion Required

FINAL ANSWER

0.125 <-- Error of Mean

(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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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

Mean Error given Specified Error of Single Measurement Formula

Error of Mean = Specified Error of a Single Measurement/(sqrt(Number of Observations))
E_m = E_s/(sqrt(n_obs))

What is a Specified Error of a Single measurement?

The specified error of a single measurement is the maximum amount of error that can be expected in a single measurement based on the specifications of the measuring instrument.

What is Mean Error?

Mean Error is the ratio of total error found in the measurement in all the observations per unit number of observations. In other words, it is the mean of the total error that occurred.

How to Calculate Mean Error given Specified Error of Single Measurement?

Mean Error given Specified Error of Single Measurement calculator uses Error of Mean = Specified Error of a Single Measurement/(sqrt(Number of Observations)) to calculate the Error of Mean, The Mean Error given Specified Error of Single Measurement formula is defined as the mean of specified error in observations. Error of Mean is denoted by E_m symbol.

How to calculate Mean Error given Specified Error of Single Measurement using this online calculator? To use this online calculator for Mean Error given Specified Error of Single Measurement, enter Specified Error of a Single Measurement (E_s) & Number of Observations (n_obs) and hit the calculate button. Here is how the Mean Error given Specified Error of Single Measurement calculation can be explained with given input values -> 0.125 = 0.25/(sqrt(4)).

FAQ

What is Mean Error given Specified Error of Single Measurement?

The Mean Error given Specified Error of Single Measurement formula is defined as the mean of specified error in observations and is represented as E_m = E_s/(sqrt(n_obs)) or Error of Mean = Specified Error of a Single Measurement/(sqrt(Number of Observations)). Specified Error of a Single Measurement is error during the separate measurement of quantity & Number of Observations refers to the number of observations taken in the given data collection.

How to calculate Mean Error given Specified Error of Single Measurement?

The Mean Error given Specified Error of Single Measurement formula is defined as the mean of specified error in observations is calculated using Error of Mean = Specified Error of a Single Measurement/(sqrt(Number of Observations)). To calculate Mean Error given Specified Error of Single Measurement, you need Specified Error of a Single Measurement (E_s) & Number of Observations (n_obs). With our tool, you need to enter the respective value for Specified Error of a Single Measurement & Number of Observations 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 Error of Mean?

In this formula, Error of Mean uses Specified Error of a Single Measurement & Number of Observations. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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