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Standard Deviation of Data Formula

GoStandard Deviation given Variance Formula

GoStandard Deviation given Coefficient of Variation Percentage Formula

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Standard Deviation of Data is the measure of how much the values in a dataset vary. It quantifies the dispersion of data points around the mean. Check FAQs

σ = \sqrt{(\frac{Σx 2}{N}) - ({(\frac{Σx}{N})}^{2})}

σ - Standard Deviation of Data?Σx² - Sum of Squares of Individual Values?N - Number of Individual Values?Σx - Sum of Individual Values?

Standard Deviation of Data Example

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

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

Here is how the Standard Deviation of Data equation looks like.

2.5 = \sqrt{(\frac{85}{10}) - ({(\frac{15}{10})}^{2})}

2.5 = \sqrt{(\frac{85}{10}) - ({(\frac{15}{10})}^{2})}

2.5 = \sqrt{(\frac{85}{10}) - ({(\frac{15}{10})}^{2})}

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Standard Deviation of Data Solution

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

FIRST Step Consider the formula

σ = \sqrt{(\frac{Σx 2}{N}) - ({(\frac{Σx}{N})}^{2})}

Next Step Substitute values of Variables

∴

σ = \sqrt{(\frac{85}{10}) - ({(\frac{15}{10})}^{2})}

Next Step Prepare to Evaluate

∴

σ = \sqrt{(\frac{85}{10}) - ({(\frac{15}{10})}^{2})}

LAST Step Evaluate

∴

σ = 2.5

Standard Deviation of Data Formula Elements

Variables

Functions

Standard Deviation of Data

Standard Deviation of Data is the measure of how much the values in a dataset vary. It quantifies the dispersion of data points around the mean.

Symbol: σ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Standard Deviation 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

Sum of Individual Values

Sum of Individual Values is the total of all the data points in a dataset.

Symbol: Σx

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Sum of Individual Values

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.

Syntax: sqrt(Number)

Other Formulas to find Standard Deviation of Data

Go Standard Deviation given Variance

σ = \sqrt{σ 2}

Go Standard Deviation given Coefficient of Variation Percentage

σ = \frac{μ \cdot CV %}{100}

Go Standard Deviation given Mean

σ = \sqrt{(\frac{Σx 2}{N}) - (μ^{2})}

Go Standard Deviation given Coefficient of Variation

σ = μ \cdot CV Ratio

Other formulas in Standard Deviation category

Go Pooled Standard Deviation

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

Go Standard Deviation of Sum of Independent Random Variables

σ (X+Y) = \sqrt{({σ X(Random)}^{2}) + ({σ Y(Random)}^{2})}

How to Evaluate Standard Deviation of Data?

Standard Deviation of Data evaluator uses Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-((Sum of Individual Values/Number of Individual Values)^2)) to evaluate the Standard Deviation of Data, Standard Deviation of Data formula is defined as the measure of how much the values in a dataset vary. It quantifies the dispersion of data points around the mean. Standard Deviation of Data is denoted by σ symbol.

How to evaluate Standard Deviation of Data using this online evaluator? To use this online evaluator for Standard Deviation of Data, enter Sum of Squares of Individual Values (Σx²), Number of Individual Values (N) & Sum of Individual Values (Σx) and hit the calculate button.

FAQs on Standard Deviation of Data

What is the formula to find Standard Deviation of Data?

The formula of Standard Deviation of Data is expressed as Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-((Sum of Individual Values/Number of Individual Values)^2)). Here is an example- 5.267827 = sqrt((85/10)-((15/10)^2)).

How to calculate Standard Deviation of Data?

With Sum of Squares of Individual Values (Σx²), Number of Individual Values (N) & Sum of Individual Values (Σx) we can find Standard Deviation of Data using the formula - Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-((Sum of Individual Values/Number of Individual Values)^2)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Standard Deviation of Data?

Here are the different ways to Calculate Standard Deviation of Data-

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

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: Unit

Standard Deviation of Data Formula

​GoStandard Deviation given Variance Formula

​GoStandard Deviation given Coefficient of Variation Percentage Formula

Standard Deviation of Data Example

Standard Deviation of Data Solution

Standard Deviation of Data Formula Elements

Other Formulas to find Standard Deviation of Data

Other formulas in Standard Deviation category

How to Evaluate Standard Deviation of Data?

FAQs on Standard Deviation of Data

Variable Name

GoStandard Deviation given Variance Formula

GoStandard Deviation given Coefficient of Variation Percentage Formula