Variance of Observations Calculator

✖Sum of square of residual variation is the value obtained by adding the squared value of residual variation.ⓘ Sum of Square of Residual Variation [ƩV²]			+10% -10%
✖Number of Observations refers to the number of observations taken in the given data collection.ⓘ Number of Observations [n_obs]			+10% -10%

✖The Variance is defined as the average of the squared differences from the Mean.ⓘ Variance of Observations [σ²]

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Formula

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Variance of Observations

Formula

`"σ"^{"2"} = "ƩV"^{"2"}/("n"_{"obs"}-1)`

Example

`"1666.667"="5000"/("4"-1)`

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Variance of Observations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Variance = Sum of Square of Residual Variation/(Number of Observations-1)
σ² = ƩV²/(n_obs-1)
This formula uses 3 Variables

Variables Used

Variance - The Variance is defined as the average of the squared differences from the Mean.
Sum of Square of Residual Variation - Sum of square of residual variation is the value obtained by adding the squared value of residual variation.
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

Sum of Square of Residual Variation: 5000 --> No Conversion Required
Number of Observations: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ² = ƩV²/(n_obs-1) --> 5000/(4-1)

Evaluating ... ...

σ² = 1666.66666666667

STEP 3: Convert Result to Output's Unit

1666.66666666667 --> No Conversion Required

FINAL ANSWER

1666.66666666667 ≈ 1666.667 <-- Variance

(Calculation completed in 00.004 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Ishita Goyal

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

Variance of Observations Formula

Variance = Sum of Square of Residual Variation/(Number of Observations-1)
σ² = ƩV²/(n_obs-1)

What is a Common Error in Leveling?

A Common Error in Leveling is the error of collimation, which occurs when the line of sight of the telescope is not perfectly horizontal.

How to Calculate Variance of Observations?

Variance of Observations calculator uses Variance = Sum of Square of Residual Variation/(Number of Observations-1) to calculate the Variance, Variance of Observations is used to measure the dispersion or spread of observed values around the mean value. it is square of standard deviation. Variance is denoted by σ² symbol.

How to calculate Variance of Observations using this online calculator? To use this online calculator for Variance of Observations, enter Sum of Square of Residual Variation (ƩV²) & Number of Observations (n_obs) and hit the calculate button. Here is how the Variance of Observations calculation can be explained with given input values -> 1666.667 = 5000/(4-1).

FAQ

What is Variance of Observations?

Variance of Observations is used to measure the dispersion or spread of observed values around the mean value. it is square of standard deviation and is represented as σ² = ƩV²/(n_obs-1) or Variance = Sum of Square of Residual Variation/(Number of Observations-1). Sum of square of residual variation is the value obtained by adding the squared value of residual variation & Number of Observations refers to the number of observations taken in the given data collection.

How to calculate Variance of Observations?

Variance of Observations is used to measure the dispersion or spread of observed values around the mean value. it is square of standard deviation is calculated using Variance = Sum of Square of Residual Variation/(Number of Observations-1). To calculate Variance of Observations, you need Sum of Square of Residual Variation (ƩV²) & Number of Observations (n_obs). With our tool, you need to enter the respective value for Sum of Square of Residual Variation & Number of Observations 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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