Variance of Data Calculator

✖Sum of Squares of Individual Values is the sum of the squared differences between each data point and the mean of the dataset.ⓘ Sum of Squares of Individual Values [Σx²]			+10% -10%
✖Number of Individual Values is the total count of distinct data points in a dataset.ⓘ Number of Individual Values [N]			+10% -10%
✖Mean of Data is the average value of all the data points in a dataset. It represents the central tendency of the data.ⓘ Mean of Data [μ]			+10% -10%

✖Variance of Data is the average of the squared differences between each data point and the mean of the dataset. It quantifies the overall variability or spread of the data points around the mean.ⓘ Variance of Data [σ²]

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Formula

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Variance of Data

Formula

`"σ"^{"2"} = ("Σx"^{"2"}/"N")-("μ"^2)`

Example

`"6.25"=("85"/"10")-(("1.5")^2)`

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Download Measures of Dispersion Formulas PDF

Variance of Data Solution

STEP 0: Pre-Calculation Summary

Formula Used

Variance of Data = (Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2)
σ² = (Σx²/N)-(μ^2)
This formula uses 4 Variables

Variables Used

Variance of Data - Variance of Data is the average of the squared differences between each data point and the mean of the dataset. It quantifies the overall variability or spread of the data points around the mean.
Sum of Squares of Individual Values - Sum of Squares of Individual Values is the sum of the squared differences between each data point and the mean of the dataset.
Number of Individual Values - Number of Individual Values is the total count of distinct data points in a dataset.
Mean of Data - Mean of Data is the average value of all the data points in a dataset. It represents the central tendency of the data.

STEP 1: Convert Input(s) to Base Unit

Sum of Squares of Individual Values: 85 --> No Conversion Required
Number of Individual Values: 10 --> No Conversion Required
Mean of Data: 1.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ² = (Σx²/N)-(μ^2) --> (85/10)-(1.5^2)

Evaluating ... ...

σ² = 6.25

STEP 3: Convert Result to Output's Unit

6.25 --> No Conversion Required

FINAL ANSWER

6.25 <-- Variance of Data

(Calculation completed in 00.004 seconds)

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< 5 Variance Calculators

Pooled Variance

Go Pooled Variance = (((Size of Sample X-1)*Variance of Sample X)+((Size of Sample Y-1)*Variance of Sample Y))/(Size of Sample X+Size of Sample Y-2)

Variance of Data

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

Variance of Sum of Independent Random Variables

Go Variance of Sum of Independent Random Variables = Variance of Random Variable X+Variance of Random Variable Y

Variance of Scalar Multiple of Random Variable

Go Variance of Scalar Multiple of Random Variable = (Scalar Value c^2)*Variance of Random Variable X

Variance given Standard Deviation

Go Variance of Data = (Standard Deviation of Data)^2

Variance of Data Formula

Variance of Data = (Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2)
σ² = (Σx²/N)-(μ^2)

What is Variance and the importance of Variance in Statistics?

Variance is a statistical tool used to analyze a statistical data. The word Variance is actually derived from the word variety that in terms of statistics means the difference among various scores and readings. Basically it is the expectation of the squared deviation of the associated random variable from its population mean or sample mean. Variance ensures accuracy as more Variance is considered good as compared to the low Variance or absolutely absence of any Variance. Variance in statistics is important as in a measurement it allows us to measure the dispersion of the set of the variables around their mean. These set of the variables are the variables that are being measured or analyzed. The presence of the Variance allows a statistician to draw some meaningful conclusion from the data. The advantage of Variance is that it treats all deviations from the mean as the same regardless of their direction.

How to Calculate Variance of Data?

Variance of Data calculator uses Variance of Data = (Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2) to calculate the Variance of Data, Variance of Data formula is defined as the average of the squared differences between each data point and the mean of the dataset. It quantifies the overall variability or spread of the data points around the mean. Variance of Data is denoted by σ² symbol.

How to calculate Variance of Data using this online calculator? To use this online calculator for Variance of Data, enter Sum of Squares of Individual Values (Σx²), Number of Individual Values (N) & Mean of Data (μ) and hit the calculate button. Here is how the Variance of Data calculation can be explained with given input values -> 6.25 = (85/10)-(1.5^2).

FAQ

What is Variance of Data?

Variance of Data formula is defined as the average of the squared differences between each data point and the mean of the dataset. It quantifies the overall variability or spread of the data points around the mean and is represented as σ² = (Σx²/N)-(μ^2) or Variance of Data = (Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2). Sum of Squares of Individual Values is the sum of the squared differences between each data point and the mean of the dataset, Number of Individual Values is the total count of distinct data points in a dataset & Mean of Data is the average value of all the data points in a dataset. It represents the central tendency of the data.

How to calculate Variance of Data?

Variance of Data formula is defined as the average of the squared differences between each data point and the mean of the dataset. It quantifies the overall variability or spread of the data points around the mean is calculated using Variance of Data = (Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2). To calculate Variance of Data, you need Sum of Squares of Individual Values (Σx²), Number of Individual Values (N) & Mean of Data (μ). With our tool, you need to enter the respective value for Sum of Squares of Individual Values, Number of Individual Values & Mean 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 Variance of Data?

In this formula, Variance of Data uses Sum of Squares of Individual Values, Number of Individual Values & Mean of Data. We can use 1 other way(s) to calculate the same, which is/are as follows -

Variance of Data = (Standard Deviation of Data)^2

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