Standard Error of Data 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%
✖Sample Size in Standard Error is the total number of individuals or items included in a specific sample. It influences the reliability and precision of statistical analyses.ⓘ Sample Size in Standard Error [N_(Error)]			+10% -10%
✖Mean of Data is the average value of all data points in a dataset. It represents the central tendency of data and is calculated by summing all values and dividing by total number of observations.ⓘ Mean of Data [μ]			+10% -10%

✖Standard Error of Data is the standard deviation of the population divided by the square root of the sample size.ⓘ Standard Error of Data given Mean [SE_Data]

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Formula

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Standard Error of Data given Mean

Formula

`"SE"_{"Data"} = sqrt(("Σx"^{"2"}/("N"_{"(Error)"}^2))-(("μ"^2)/"N"_{"(Error)"}))`

Example

`"2.5"=sqrt(("85000"/(("100")^2))-((("15")^2)/"100"))`

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Download Errors, Sum of Squares, Degrees of Freedom and Hypothesis Testing Formulas PDF

Standard Error of Data given Mean Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standard Error of Data = sqrt((Sum of Squares of Individual Values/(Sample Size in Standard Error^2))-((Mean of Data^2)/Sample Size in Standard Error))
SE_Data = sqrt((Σx²/(N_(Error)^2))-((μ^2)/N_(Error)))
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 Error of Data - Standard Error of Data is the standard deviation of the population divided by the square root of the sample size.
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.
Sample Size in Standard Error - Sample Size in Standard Error is the total number of individuals or items included in a specific sample. It influences the reliability and precision of statistical analyses.
Mean of Data - Mean of Data is the average value of all data points in a dataset. It represents the central tendency of data and is calculated by summing all values and dividing by total number of observations.

STEP 1: Convert Input(s) to Base Unit

Sum of Squares of Individual Values: 85000 --> No Conversion Required
Sample Size in Standard Error: 100 --> No Conversion Required
Mean of Data: 15 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

SE_Data = sqrt((Σx²/(N_(Error)^2))-((μ^2)/N_(Error))) --> sqrt((85000/(100^2))-((15^2)/100))

Evaluating ... ...

SE_Data = 2.5

STEP 3: Convert Result to Output's Unit

2.5 --> No Conversion Required

FINAL ANSWER

2.5 <-- Standard Error of Data

(Calculation completed in 00.004 seconds)

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

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< 7 Errors Calculators

Standard Error of Difference of Means

Go Standard Error of Difference of Means = sqrt(((Standard Deviation of Sample X^2)/Size of Sample X in Standard Error)+((Standard Deviation of Sample Y^2)/Size of Sample Y in Standard Error))

Standard Error of Data given Mean

Go Standard Error of Data = sqrt((Sum of Squares of Individual Values/(Sample Size in Standard Error^2))-((Mean of Data^2)/Sample Size in Standard Error))

Standard Error of Proportion

Go Standard Error of Proportion = sqrt((Sample Proportion*(1-Sample Proportion))/Sample Size in Standard Error)

Residual Standard Error of Data given Degrees of Freedom

Go Residual Standard Error of Data = sqrt(Residual Sum of Squares in Standard Error/Degrees of Freedom in Standard Error)

Residual Standard Error of Data

Go Residual Standard Error of Data = sqrt(Residual Sum of Squares in Standard Error/(Sample Size in Standard Error-1))

Standard Error of Data given Variance

Go Standard Error of Data = sqrt(Variance of Data in Standard Error/Sample Size in Standard Error)

Standard Error of Data

Go Standard Error of Data = Standard Deviation of Data/sqrt(Sample Size in Standard Error)

Standard Error of Data given Mean Formula

What is Standard Error and it's importance?

In Statistics and data analysis standard error has great importance. The term "standard error" is used to refer to the standard deviation of various sample statistics, such as the mean or median. For example, the "standard error of the mean" refers to the standard deviation of the distribution of sample means taken from a population. The smaller the standard error, the more representative the sample will be of the overall population.
The relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size. The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.

How to Calculate Standard Error of Data given Mean?

Standard Error of Data given Mean calculator uses Standard Error of Data = sqrt((Sum of Squares of Individual Values/(Sample Size in Standard Error^2))-((Mean of Data^2)/Sample Size in Standard Error)) to calculate the Standard Error of Data, Standard Error of Data given Mean formula is defined as the standard deviation of the population divided by the square root of the sample size, and calculated using the mean of the data. Standard Error of Data is denoted by SE_Data symbol.

How to calculate Standard Error of Data given Mean using this online calculator? To use this online calculator for Standard Error of Data given Mean, enter Sum of Squares of Individual Values (Σx²), Sample Size in Standard Error (N_(Error)) & Mean of Data (μ) and hit the calculate button. Here is how the Standard Error of Data given Mean calculation can be explained with given input values -> 19.04673 = sqrt((85000/(100^2))-((15^2)/100)).

FAQ

What is Standard Error of Data given Mean?

Standard Error of Data given Mean formula is defined as the standard deviation of the population divided by the square root of the sample size, and calculated using the mean of the data and is represented as SE_Data = sqrt((Σx²/(N_(Error)^2))-((μ^2)/N_(Error))) or Standard Error of Data = sqrt((Sum of Squares of Individual Values/(Sample Size in Standard Error^2))-((Mean of Data^2)/Sample Size in Standard Error)). Sum of Squares of Individual Values is the sum of the squared differences between each data point and the mean of the dataset, Sample Size in Standard Error is the total number of individuals or items included in a specific sample. It influences the reliability and precision of statistical analyses & Mean of Data is the average value of all data points in a dataset. It represents the central tendency of data and is calculated by summing all values and dividing by total number of observations.

How to calculate Standard Error of Data given Mean?

Standard Error of Data given Mean formula is defined as the standard deviation of the population divided by the square root of the sample size, and calculated using the mean of the data is calculated using Standard Error of Data = sqrt((Sum of Squares of Individual Values/(Sample Size in Standard Error^2))-((Mean of Data^2)/Sample Size in Standard Error)). To calculate Standard Error of Data given Mean, you need Sum of Squares of Individual Values (Σx²), Sample Size in Standard Error (N_(Error)) & Mean of Data (μ). With our tool, you need to enter the respective value for Sum of Squares of Individual Values, Sample Size in Standard Error & 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 Error of Data?

In this formula, Standard Error of Data uses Sum of Squares of Individual Values, Sample Size in Standard Error & Mean of Data. We can use 2 other way(s) to calculate the same, which is/are as follows -

Standard Error of Data = sqrt(Variance of Data in Standard Error/Sample Size in Standard Error)
Standard Error of Data = Standard Deviation of Data/sqrt(Sample Size in Standard Error)

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