Standard Deviation given Mean 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%

✖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.ⓘ Standard Deviation given Mean [σ]

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Formula

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Standard Deviation given Mean

Formula

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

Example

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

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Standard Deviation given Mean Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2))
σ = sqrt((Σx²/N)-(μ^2))
This formula uses 1 Functions, 4 Variables

Functions Used

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., sqrt(Number)

Variables Used

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.
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

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

Evaluating ... ...

σ = 2.5

STEP 3: Convert Result to Output's Unit

2.5 --> No Conversion Required

FINAL ANSWER

2.5 <-- Standard Deviation of Data

(Calculation completed in 00.005 seconds)

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Created by Nishan Poojary

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

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< 7 Standard Deviation Calculators

Pooled Standard Deviation

Go Pooled Standard Deviation = sqrt((((Size of Sample X-1)*(Standard Deviation of Sample X^2))+((Size of Sample Y-1)*(Standard Deviation of Sample Y^2)))/(Size of Sample X+Size of Sample Y-2))

Standard Deviation of Data

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

Standard Deviation given Mean

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

Standard Deviation of Sum of Independent Random Variables

Go Standard Deviation of Sum of Random Variables = sqrt((Standard Deviation of Random Variable X^2)+(Standard Deviation of Random Variable Y^2))

Standard Deviation given Coefficient of Variation Percentage

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

Standard Deviation given Coefficient of Variation

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

Standard Deviation given Variance

Go Standard Deviation of Data = sqrt(Variance of Data)

Standard Deviation given Mean Formula

Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2))
σ = sqrt((Σx²/N)-(μ^2))

What is Standard Deviation in Statistics?

In Statistics, the Standard Deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. The Standard Deviation of a random variable, sample, statistical population, data set, or probability distribution is defined and calculated as the square root of its variance.

How to Calculate Standard Deviation given Mean?

Standard Deviation given Mean calculator uses Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2)) to calculate 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 calculate Standard Deviation given Mean using this online calculator? To use this online calculator 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. Here is how the Standard Deviation given Mean calculation can be explained with given input values -> 5.267827 = sqrt((85/10)-(1.5^2)).

FAQ

What is Standard Deviation given Mean?

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 and is represented as σ = sqrt((Σx²/N)-(μ^2)) or Standard Deviation of Data = sqrt((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 Standard Deviation given Mean?

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 is calculated using Standard Deviation of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Mean of Data^2)). To calculate Standard Deviation given Mean, 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 Standard Deviation of Data?

In this formula, Standard Deviation of Data uses Sum of Squares of Individual Values, Number of Individual Values & Mean of Data. We can use 4 other way(s) to calculate the same, which is/are as follows -

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

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