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Standard Error Calculator

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Standard Error Calculator

Standard Error Calculator is used to determine the standard error of the group data or sample data using the standard deviation and sample size. 

What is Standard Error?

The standard error is a statistical term that measures the variability or uncertainty in the estimates or measurements of a statistical sample variation. In simple terms, standard error quantifies the average amount of variation or error we can expect in the estimate of a population parameter based on a sample.

 

It provides an indication of how reliable the sample statistic is in representing the population parameters estimation. It measures the precision or dispersion of the sample statistic with the true population parameter.

 

The standard error in numerical form is calculated using the standard deviation of the sample data and the sample size. It is simply denoted as “SE”.

The formula for Standard Error

The formula of standard error in mathematical form is stated below.

Standard Error (SE) = (Standard Deviation of the Sample) / √Sample Size

standard error

 Where,

  • σ = Standard deviation,
  • n = Sample Size

How to find the numerical value of Standard Error?

Example 1:

If the sample size of statistical data is 5 and the sample data is 34, 12, 13, 15, and 10 then find the Standard error.

Solution:

Step 1: Write the data from the given sample data.

Input Data = {34, 12, 13, 15, 10}, sample size = n = 5

Step 2: Write the formula of the Standard error.

Standard error = σ/√n

Step 3: Write the formula of Standard deviation.

STD (σ) = √(∑ (x - x̄)2/n – 1)

Step 4: Using the formula of mean find the standard error.

x̄ = (Sum of all Values Number of values)/sample size

x̄ = (34+12+13+15+105)/5

x̄ = 845/5

x̄ = 16.8

∑(x - x̄)2 = ( 34 - 16.8 )2 + ( 12 - 16.8 )2 + ( 13 - 16.8 )2 + ( 15 - 16.8 )2 + ( 10 - 16.8 )2

∑ (x-x̄)2 = (17.2)2 + (4.8)2 + (3.8)2 + (1.8)2 + (-6.8)2

∑ (x - x̄)2 = 382.8

Step 5: Put the value in the formula of “Step 3” and simplify.

STD (σ) = √{(∑ (x - x̄)2)/(n – 1)}

 = √ {382.8/(5 – 1)}

 = √ {382.8/4}

 = √ 95.7

STD (σ) = 9.78264

Step 6: Finally, put the above values in the Standard error formula.

SE =  9.78264/√5

SE = 4.37493

Example 2:

If the standard deviation is 56 and the sample size is 6 then find the standard error.

Solution:

Step 1: Write the data from the above conditions.

σ = 56, n = 6.

Step 2: Write the formula of standard error.

SE = σ/√n

Step 3: Put the values in the above formula.

Standard error (SE) = 56/√5

SE = 22.8619

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