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Standard Deviation given Mean 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}) - (μ^{2})}

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

Standard Deviation given Mean Example

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Here is how the Standard Deviation given Mean equation looks like with Values.

Here is how the Standard Deviation given Mean equation looks like with Units.

Here is how the Standard Deviation given Mean equation looks like.

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

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

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

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Standard Deviation given Mean Solution

Follow our step by step solution on how to calculate Standard Deviation given Mean?

FIRST Step Consider the formula

σ = \sqrt{(\frac{Σx 2}{N}) - (μ^{2})}

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

LAST Step Evaluate

∴

σ = 2.5

Standard Deviation given Mean 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

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

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 Coefficient of Variation

σ = μ \cdot CV Ratio

Go Standard Deviation of Data

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

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 given Mean?

Standard Deviation given Mean evaluator uses Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2)) to evaluate the Standard Deviation of Data, Standard Deviation given Mean 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, and calculated using the mean of the given data. Standard Deviation of Data is denoted by σ symbol.

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

FAQs on Standard Deviation given Mean

What is the formula to find Standard Deviation given Mean?

The formula of Standard Deviation given Mean is expressed as Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2)). Here is an example- 5.267827 = sqrt((85/10)-(1.5^2)).

How to calculate Standard Deviation given Mean?

With Sum of Squares of Individual Values (Σx²), Number of Individual Values (N) & Mean of Data (μ) we can find Standard Deviation given Mean using the formula - Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^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=Mean of Data*Coefficient of Variation Ratio

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: Unit

Standard Deviation given Mean Formula

​GoStandard Deviation given Variance Formula

​GoStandard Deviation given Coefficient of Variation Percentage Formula

Standard Deviation given Mean Example

Standard Deviation given Mean Solution

Standard Deviation given Mean Formula Elements

Other Formulas to find Standard Deviation of Data

Other formulas in Standard Deviation category

How to Evaluate Standard Deviation given Mean?

FAQs on Standard Deviation given Mean

Variable Name

GoStandard Deviation given Variance Formula

GoStandard Deviation given Coefficient of Variation Percentage Formula