Mean of Data given Variance Calculator

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✖Sum of Squares of Individual Values is the total sum of squares of all individual values of the random variable in the given statistical data.ⓘ Sum of Squares of Individual Values [Σx²]			+10% -10%
✖Number of Individual Values is the total number of individual values of the random variable in the given statistical data or population or sample.ⓘ Number of Individual Values [N]			+10% -10%
✖Variance of Data is the expectation of the squared deviation of the random variable associated with the given statistical data from its population mean or sample mean.ⓘ Variance of Data [V]			+10% -10%

✖Mean of Data is the average of the individual values in the given statistical data.ⓘ Mean of Data given Variance [μ]

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Formula

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Mean of Data given Variance

Formula

`"μ" = sqrt(("Σx"^{"2"}/"N")-"V")`

Example

`"6.964194"=sqrt(("1000"/"16")-"14")`

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Mean of Data given Variance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-Variance of Data)
μ = sqrt((Σx²/N)-V)
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - Squre root function, sqrt(Number)

Variables Used

Mean of Data - Mean of Data is the average of the individual values in the given statistical data.
Sum of Squares of Individual Values - Sum of Squares of Individual Values is the total sum of squares of all individual values of the random variable in the given statistical data.
Number of Individual Values - Number of Individual Values is the total number of individual values of the random variable in the given statistical data or population or sample.
Variance of Data - Variance of Data is the expectation of the squared deviation of the random variable associated with the given statistical data from its population mean or sample mean.

STEP 1: Convert Input(s) to Base Unit

Sum of Squares of Individual Values: 1000 --> No Conversion Required
Number of Individual Values: 16 --> No Conversion Required
Variance of Data: 14 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

μ = sqrt((Σx²/N)-V) --> sqrt((1000/16)-14)

Evaluating ... ...

μ = 6.96419413859206

STEP 3: Convert Result to Output's Unit

6.96419413859206 --> No Conversion Required

FINAL ANSWER

6.96419413859206 <-- Mean of Data

(Calculation completed in 00.016 seconds)

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Home » Math » Statistics » Measures of Central Tendency » Mean » Mean of Data given Variance

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Created by Nishan Poojary

Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

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< 7 Mean Calculators

Combined Mean of Multiple Data

Go Combined Mean of Multiple Data = ((Sample Size of Random Variable X*Mean of Random Variable X)+(Sample Size of Random Variable Y*Mean of Random Variable Y))/(Sample Size of Random Variable X+Sample Size of Random Variable Y)

Mean of Data given Standard Deviation

Go Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Standard Deviation of Data^2))

Mean of Data given Variance

Go Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-Variance of Data)

Mean of Data given Coefficient of Variation Percentage

Go Mean of Data = (Standard Deviation of Data/Coefficient of Variation Percentage)*100

Mean of Data given Coefficient of Variation Ratio

Go Mean of Data = Standard Deviation of Data/Coefficient of Variation Ratio

Mean of Data

Go Mean of Data = Sum of Individual Values/Number of Individual Values

Mean of Data given Median and Mode

Go Mean of Data = ((3*Median of Data)-Mode of Data)/2

Mean of Data given Variance Formula

Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-Variance of Data)
μ = sqrt((Σx²/N)-V)

What is Mean and it's importance?

In Statistics, the most commonly used measure of central tendency is the Mean. The word 'mean' is the statistical term used for the 'average'. The mean can be used to represent the typical value and therefore serves as a yardstick for all observations. For example, if we would like to know how many hours on average an employee spends at training in a year, we can find the mean training hours of a group of employees. One of the main importance of the mean from the other measures of central tendencies is that, mean takes into consideration all the elements in the given data. It calculates the average value of the set of data. It cannot be an accurate measurement for skewed distribution. If the mean is equal to the median, then the distribution is normal.

How to Calculate Mean of Data given Variance?

Mean of Data given Variance calculator uses Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-Variance of Data) to calculate the Mean of Data, Mean of Data given Variance formula is defined as the average of the individual values in the given statistical data, and calculated using the variance of the data. Mean of Data is denoted by μ symbol.

How to calculate Mean of Data given Variance using this online calculator? To use this online calculator for Mean of Data given Variance, enter Sum of Squares of Individual Values (Σx²), Number of Individual Values (N) & Variance of Data (V) and hit the calculate button. Here is how the Mean of Data given Variance calculation can be explained with given input values -> 6.964194 = sqrt((1000/16)-14).

FAQ

What is Mean of Data given Variance?

Mean of Data given Variance formula is defined as the average of the individual values in the given statistical data, and calculated using the variance of the data and is represented as μ = sqrt((Σx²/N)-V) or Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-Variance of Data). Sum of Squares of Individual Values is the total sum of squares of all individual values of the random variable in the given statistical data, Number of Individual Values is the total number of individual values of the random variable in the given statistical data or population or sample & Variance of Data is the expectation of the squared deviation of the random variable associated with the given statistical data from its population mean or sample mean.

How to calculate Mean of Data given Variance?

Mean of Data given Variance formula is defined as the average of the individual values in the given statistical data, and calculated using the variance of the data is calculated using Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-Variance of Data). To calculate Mean of Data given Variance, you need Sum of Squares of Individual Values (Σx²), Number of Individual Values (N) & Variance of Data (V). With our tool, you need to enter the respective value for Sum of Squares of Individual Values, Number of Individual Values & Variance of Data 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 Mean of Data?

In this formula, Mean of Data uses Sum of Squares of Individual Values, Number of Individual Values & Variance of Data. We can use 5 other way(s) to calculate the same, which is/are as follows -

Mean of Data = ((3*Median of Data)-Mode of Data)/2
Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Standard Deviation of Data^2))
Mean of Data = Standard Deviation of Data/Coefficient of Variation Ratio
Mean of Data = (Standard Deviation of Data/Coefficient of Variation Percentage)*100
Mean of Data = Sum of Individual Values/Number of Individual Values

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