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Variance of Data Formula

GoVariance given Standard Deviation Formula

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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. Check FAQs

σ 2 = (\frac{Σx 2}{N}) - (μ^{2})

σ² - Variance of Data?Σx² - Sum of Squares of Individual Values?N - Number of Individual Values?μ - Mean of Data?

Variance of Data Example

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Here is how the Variance of Data equation looks like with Values.

Here is how the Variance of Data equation looks like with Units.

Here is how the Variance of Data equation looks like.

6.25 = (\frac{85}{10}) - ({1.5}^{2})

6.25 = (\frac{85}{10}) - ({1.5}^{2})

6.25 = (\frac{85}{10}) - ({1.5}^{2})

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Variance of Data Solution

Follow our step by step solution on how to calculate Variance of Data?

FIRST Step Consider the formula

σ 2 = (\frac{Σx 2}{N}) - (μ^{2})

Next Step Substitute values of Variables

∴

σ 2 = (\frac{85}{10}) - ({1.5}^{2})

Next Step Prepare to Evaluate

∴

σ 2 = (\frac{85}{10}) - ({1.5}^{2})

LAST Step Evaluate

∴

σ 2 = 6.25

Variance of Data Formula Elements

Variables

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.

Symbol: σ²

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Variance of Data

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.

Symbol: Σx²

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Sum of Squares of Individual Values

Number of Individual Values

Number of Individual Values is the total count of distinct data points in a dataset.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Individual Values

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.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Mean of Data

Other Formulas to find Variance of Data

Go Variance given Standard Deviation

σ 2 = {(σ)}^{2}

Other formulas in Variance category

Go Variance of Scalar Multiple of Random Variable

V cX = (c^{2}) \cdot σ 2 Random X

Go Variance of Sum of Independent Random Variables

σ 2 Sum = σ 2 Random X + σ 2 Random Y

Go Pooled Variance

V Pooled = \frac{((N X - 1) \cdot σ 2 X) + ((N Y - 1) \cdot σ 2 Y)}{N X + N Y - 2}

How to Evaluate Variance of Data?

Variance of Data evaluator uses Variance of Data = (Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2) to evaluate 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 evaluate Variance of Data using this online evaluator? To use this online evaluator 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.

FAQs on Variance of Data

What is the formula to find Variance of Data?

The formula of Variance of Data is expressed as Variance of Data = (Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2). Here is an example- 6.25 = (85/10)-(1.5^2).

How to calculate Variance of Data?

With Sum of Squares of Individual Values (Σx²), Number of Individual Values (N) & Mean of Data (μ) we can find Variance of Data using the formula - Variance of Data = (Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2).

What are the other ways to Calculate Variance of Data?

Here are the different ways to Calculate Variance of Data-

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

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Variance of Data Formula

​GoVariance given Standard Deviation Formula

Variance of Data Example

Variance of Data Solution

Variance of Data Formula Elements

Other Formulas to find Variance of Data

Other formulas in Variance category

How to Evaluate Variance of Data?

FAQs on Variance of Data

Variable Name

GoVariance given Standard Deviation Formula