Mean of Data given Standard Deviation 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_Values]			+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 of Data [σ]			+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 given Standard Deviation [Mean]

⎘ Copy

👎

Formula

✖

Mean of Data given Standard Deviation

Formula

`"Mean" = sqrt(("Σx"^{"2"}/"N"_{"Values"})-("σ"^2))`

Example

`"75"=sqrt(("62500"/"10")-(("25")^2))`

Calculator

LaTeX

Reset

👍

Download Measures of Central Tendency Formulas PDF

Mean of Data given Standard Deviation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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

Sum of Squares of Individual Values: 62500 --> No Conversion Required
Number of Individual Values: 10 --> No Conversion Required
Standard Deviation of Data: 25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Mean = sqrt((Σx²/N_Values)-(σ^2)) --> sqrt((62500/10)-(25^2))

Evaluating ... ...

Mean = 75

STEP 3: Convert Result to Output's Unit

75 --> No Conversion Required

FINAL ANSWER

75 <-- Mean of Data

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Statistics » Measures of Central Tendency » Mean » Mean of Data given Standard Deviation

Credits

Created by Anirudh Singh

National Institute of Technology (NIT), Jamshedpur

Anirudh Singh has created this Calculator and 300+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 7 Mean Calculators

Combined Mean of Multiple Data

Go Combined Mean of Multiple Data = ((Sample Size of Random Variable X*Mean of Random Variable X)+(Sample Size of Random Variable Y*Mean of Random Variable Y))/(Sample Size of Random Variable X+Sample Size of Random Variable Y)

Mean of Data given Standard Deviation

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

Mean of Data given Variance

Go Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-Variance of Data)

Mean of Data given Coefficient of Variation Percentage

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

Mean of Data

Go Mean of Data = Sum of Individual Values/Number of Individual Values

Mean of Data given Coefficient of Variation

Go Mean of Data = Standard Deviation of Data/Coefficient of Variation

Mean of Data given Median and Mode

Go Mean of Data = ((3*Median of Data)-Mode of Data)/2

Mean of Data given Standard Deviation Formula

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

What is Mean and it's importance?

In Statistics, the most commonly used measure of central tendency is the Mean. The word 'mean' is the statistical term used for the 'average'. The mean can be used to represent the typical value and therefore serves as a yardstick for all observations. For example, if we would like to know how many hours on average an employee spends at training in a year, we can find the mean training hours of a group of employees. One of the main importance of the mean from the other measures of central tendencies is that, mean takes into consideration all the elements in the given data. It calculates the average value of the set of data. It cannot be an accurate measurement for skewed distribution. If the mean is equal to the median, then the distribution is normal.

How to Calculate Mean of Data given Standard Deviation?

Mean of Data given Standard Deviation calculator uses Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Standard Deviation of Data^2)) to calculate the Mean of Data, Mean of Data given Standard Deviation formula is defined as the average value of all the data points in a dataset. It represents the central tendency of the data, and calculated using the standard deviation of the data. Mean of Data is denoted by Mean symbol.

How to calculate Mean of Data given Standard Deviation using this online calculator? To use this online calculator for Mean of Data given Standard Deviation, enter Sum of Squares of Individual Values (Σx²), Number of Individual Values (N_Values) & Standard Deviation of Data (σ) and hit the calculate button. Here is how the Mean of Data given Standard Deviation calculation can be explained with given input values -> 78.95568 = sqrt((62500/10)-(25^2)).

FAQ

What is Mean of Data given Standard Deviation?

Mean of Data given Standard Deviation formula is defined as the average value of all the data points in a dataset. It represents the central tendency of the data, and calculated using the standard deviation of the data and is represented as Mean = sqrt((Σx²/N_Values)-(σ^2)) or Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Standard Deviation 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 & 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 Mean of Data given Standard Deviation?

Mean of Data given Standard Deviation formula is defined as the average value of all the data points in a dataset. It represents the central tendency of the data, and calculated using the standard deviation of the data is calculated using Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-(Standard Deviation of Data^2)). To calculate Mean of Data given Standard Deviation, you need Sum of Squares of Individual Values (Σx²), Number of Individual Values (N_Values) & Standard Deviation of Data (σ). With our tool, you need to enter the respective value for Sum of Squares of Individual Values, Number of Individual Values & 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 Mean of Data?

In this formula, Mean of Data uses Sum of Squares of Individual Values, Number of Individual Values & Standard Deviation of Data. We can use 5 other way(s) to calculate the same, which is/are as follows -

Mean of Data = ((3*Median of Data)-Mode of Data)/2
Mean of Data = Standard Deviation of Data/Coefficient of Variation
Mean of Data = (Standard Deviation of Data/Coefficient of Variation Percentage)*100
Mean of Data = Sum of Individual Values/Number of Individual Values
Mean of Data = sqrt((Sum of Squares of Individual Values/Number of Individual Values)-Variance of Data)

Home

FREE PDFs

🔍 Search