Standard Error Calculator

The Standard Error (SE) of statistical data is the approximate standard deviation of sample statistics. In simple words, the standard error of the mean refers to the standard deviation of sample means.

Usually, the sample distribution represents a sample population. A smaller standard error thus indicates a more representative sample of the overall population or the true mean.

Standard Error Formula

The formula to calculate the standard error of mean is as given below: 

SE_x = S/√n

Where,

• SE = Standard Error
• S = Standard Deviation
• n = Total Size

How to Calculate Standard Error?

Estimating the mean of a given set of numbers is quite easy. We have been using it from an early age onwards. However, calculating the sample mean dispersion from the true meaning is different. 

With a Standard Error Calculator, it becomes easy to find the standard error without going through the formulas. By using the calculator, you can simply find the standard error of a long set of statistical data within a fraction of seconds. Now, let us take a look at how this is done using formula and know the easiness of using a standard error calculator. 

Steps for Finding Standard Error of the Mean

You need to work out the formula to find the standard error. Imagine you have 10 different values with you. To find the standard error, you need to follow the below steps.

1. Solve the mean value of the set of numbers.
2. Find the difference between every number and the mean of it. 
3. Calculate the square of each deviation from the mean. 
4. Sum up the squares deviations.
5. Take the result of step 4 and Divide by one less than the sample size (n-1, that is, the number of measurements minus one)
6. Compute the square root of the latter, which is the standard error of the mean.

This is how you calculate the standard error of the mean manually using the standard error formula. To make it simple, you can use our free online standard error calculator and find the results in less time. 

Now, let us take an example.

Solved Example on Standard Error (SE) from Mean & Standard Deviation

Example: 

Let the numbers be 10, 20, 30, and 40. Find the standard error of the data set?

Solution: 

Mean = (10 + 20 + 30 + 40)/4 = 100/4 = 25

Mean = 25

Standard Deviation (σ) = √(1/4 - 1) x ((10 - 25)^2 + ( 20 - 25)^2 + ( 30 - 25)^2 + ( 40 - 25)^2)
= √(1/3) x ((-15)^2 + (-5)^2 + (5)^2 + (15)^2)
= √(0.3333) x ((225) + (25) + (25) + (225))
= √(0.3333) x 500
= √166.6667

Standard Deviation σ = 12.9099

Standard Error = σ√n
= 12.9099√4

= 12.90992

Standard Error = 6.455

This is how we find standard error of mean by using the direct formula.

Finding standard error of mean of decimal numbers using steps

Now let’s see how to find standard error of mean of decimal numbers using steps.

Example:

Find the standard error of mean of decimal numbers [5.5, 5.8, 6.1, 5.4, 5.5, 5.4, 5.9, 5.6, 5.9, 5.5]

1. Find the mean: x̄ = (5.5+5.8+6.1+5.4+5.5+5.4+5.9+5.6+5.9+5.5) / 10 = 56.6/10 = 5.66.
2. Find the difference: (xᵢ - x̄): [-0.16, 0.14, 0.44, -0.26, -0.16, -0.26, 0.24, -0.6, 0.24, -0.16].
3. Find the square: [0.0256, 0.0196, 0.1936, 0.0676, 0.0256, 0.0676, 0.0576, 0.0036, 0.0576, 0.0256].
4. Sum of squares: 0.0256 + 0.0196 + 0.1936 + 0.0676 + 0.0256 + 0.0676 + 0.0576 + 0.0036 + 0.0576 + 0.0256 = 0.544.
5. Make a fraction and 90 (that is N*(N-1)=10*9): 0.544 / 90 = 0.0060.
6. SEM = √0.0060 = 0.078.

This is how to calculate the standard error of the mean of decimal numbers. 

Standard error of mean is usually used to find the height, weight, or length of students, people, or objects.

To find the standard error of the mean of a given population, we generally use these methods. But our arithemeticcalculator.com provided handy standard error calculator now makes it easy to find the results.

FAQs on Free standard error calculator from mean and standard deviation

1. How can I calculate standard error of mean easily?

You can either find the standard error of mean using the formula or can use a standard error calculator. Using the calculator is easy as it gives the results once after typing the numbers.

2. How should I calculate standard deviation?

Calculate the mean and find the difference between each number and the mean. Find the squares of each and add to get the SD result.

3. How to calculate standard error in Excel?

The standard error is calculated by dividing the standard deviation by the square root of the total number of samples. Translate it to Excel formula as Standard Error is equal to STDEV (sampling range)/SQRT(COUNT(sampling range)).

4. Can I use decimal numbers to find standard error of mean?

Yes, you are allowed to give decimals as input for finding the standard error of mean in the standard error calculator as it provides results in a matter of seconds.