Variance given Standard Deviation Calculator

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Variance Quartile Deviation Standard Deviation

✖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 of Data [σ]

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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.ⓘ Variance given Standard Deviation [σ²]

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Variance given Standard Deviation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Variance of Data = (Standard Deviation of Data)^2
σ² = (σ)^2
This formula uses 2 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.
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.

STEP 1: Convert Input(s) to Base Unit

Standard Deviation of Data: 2.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ² = (σ)^2 --> (2.5)^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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Created by Anirudh Singh

National Institute of Technology (NIT), Jamshedpur

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< Variance Calculators

Variance of Data

LaTeX 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

LaTeX 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

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

Variance given Standard Deviation

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

Variance given Standard Deviation Formula

LaTeX Go

Variance of Data = (Standard Deviation of Data)^2
σ² = (σ)^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 given Standard Deviation?

Variance given Standard Deviation calculator uses Variance of Data = (Standard Deviation of Data)^2 to calculate the Variance of Data, Variance given Standard Deviation 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 calculated using the standard deviation of the given data. Variance of Data is denoted by σ² symbol.

How to calculate Variance given Standard Deviation using this online calculator? To use this online calculator for Variance given Standard Deviation, enter Standard Deviation of Data (σ) and hit the calculate button. Here is how the Variance given Standard Deviation calculation can be explained with given input values -> 6.25 = (2.5)^2.

FAQ

What is Variance given Standard Deviation?

Variance given Standard Deviation 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 calculated using the standard deviation of the given data and is represented as σ² = (σ)^2 or Variance of Data = (Standard Deviation of Data)^2. 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.

How to calculate Variance given Standard Deviation?

Variance given Standard Deviation 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 calculated using the standard deviation of the given data is calculated using Variance of Data = (Standard Deviation of Data)^2. To calculate Variance given Standard Deviation, you need Standard Deviation of Data (σ). With our tool, you need to enter the respective value for Standard Deviation 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 Standard Deviation of Data. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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