Standard Error Calculator

Standard error calculator helps you to calculate the sample mean dispersion from the given raw data set or from the sample mean for statistical data analysis.

Give a complete read to this useful & important content to know about the basic terms, formulas and calculations related to the standard error.

What is the Standard Error Formula?

The standard error equation is as follows:

$$ S.E = \frac{s}{\sqrt{n}} $$

S.E = s/√n

Where,

s is the standard deviation of the numbers.

n is the number of samples.

When You Have Raw Data:

When you have raw data points, first you need to find the standard deviation and sample mean of the data. The formulas for standard deviation & population mean are:

S.D = √⅀(Xi -µ)2/N-1

Where,

Xi is each value in the data set.

µ is the mean of all values in the data set.

N is the total number of values in the data set.

Now, the formula for sample mean is:

µ =X1 + X2 + X3 + X4 +…….+ XN / N

These are the formulas which are also used by this online standard error calculator for the estimated results of your problem. Just read on, we have the complete step by step manual example for both the calculations.

Difference Between SEM & SD:

The SD and SEM both are used in statistical studies, in Finance, biology, engineering, psychology, medicine etc. The standard deviation (SD) & standard error of the mean (SEM) are used to represent the characteristics of the sample data and explain statistical analysis results.

Remember that, SD & SEM both are different, each have its own meaning. Standard deviation (SD) is the measure of dispersion of the individual data values. In simple words, SD determines how the sample data represents the mean accurately.

While, the SEM includes the statistical results of a particular value or sampling distribution. The SEM is the SD of theoretical distribution of sample means. Here you get a central tendency calculator that helps you to calculate mean, median. mode and range of the given date set.

You can try the online standard error of the mean calculator that allows you to find out the standard error from the sample mean & standard deviation.

Applications of Standard Error:

It is the most important and widely used measure in Statistics to determine the reliability of the sample data or mean. The major applications of standard error include, test of significance or hypothesis testing for large & small sample size (Z & t statistic) to measure the reliability of sample, to determine the confidence interval for sample.

It’s a statistical measure calculated from the sampling distribution where the large size samples minimize the SE of the statistic & vice versa. For the accurate & quick results, people may use this standard error calculator to determine the results with complete step-by-step calculations.

How to Calculate Standard Error Manually (Step-by-Step):

The formula for standard error is discussed earlier. Now, we have an example with complete step-by-step calculations.

Example:

Let’s have raw data 12, 23, 45, 33, 65, 54. Find the standard error of the given data?

Solution:

The formula to calculate SE is:

S.E = s/√n

Step1:

First of all, we have to calculate the mean of the data. The formula is:

µ =X1 + X2 + X3 + X4 +…….+ XN / N

So,

µ =12 + 23 + 45 + 33 + 65 + 54/ 6

µ =232/ 6

µ =38.66

Step 2:

Then, determine the standard deviation of the data.

S.D = √⅀(Xi -µ)2/N-1

Here,

µ = 38.66

So,

S.D = √⅀(Xi -µ)2/N-1

S.D = √ {(12-38.66)2 + (23-38.66)2 + (45-38.66)2 + (33-38.66)2 + (65-38.66)2 + (54-38.66)2}/6-1

S.D = √ {(-26.66)2 + (-15.66)2 + (6.34)2 + (-5.66)2 + (26.34)2 + (15.34)2}/5

S.D = √ {710.75 + 245.23 + 40.19 + 32.03 + 693.79 + 235.31}/5

S.D = √1957.3/5

S.D = √391.46

S.D = 19.7

Step 3:

Now,

S.E = s/√n

S.E = 19.7/√6

S.E = 19.7/2.44

S.E = 8.07

You can use the online standard error calculator to verify your answers with complete step-by-step calculations.

How to Find Standard Error With Standard Error Calculator:

Calculating standard error becomes very easy with this online sem calculator. Give a detailed calculation of the standard error.

Swipe on!

Calculations from the Raw Data:

To calculate the standard error from the raw data, just stick to these following points:

Inputs:

• First of all, enter the data points in the designated field separated with commas.
• Then, hit the calculate button.

Outputs:

The calculator will show:

• Standard Error of the numbers.
• Total numbers.
• Sum of the numbers.
• Mean of the numbers.
• Standard deviation between the numbers.
• Complete Step-by-Step calculation.

Calculations from the Summary Data:

Inputs:

• Firstly, enter the standard deviation between the numbers.
• Very next, plug-in the total number of samples (n) in the designated field.
• Lastly, click on the calculate button.

Outputs:

The tool shows:

• Standard Error of the numbers.
• Complete Step-by-Step calculation.

Simply, use the online standard error calculator for the complete step-by-step calculations from both raw data & from summary of the data.

Frequently Ask Questions (FAQ’s):

What is Standard Error?

It is a statistical term that measures the accuracy of the sample by using the standard deviation. The SE of a statistic is the standard deviation of the statistical sample population. In Statistics, the sample mean diverges from the actual mean and this deviation is the standard error of the mean.

What is a good value for standard error?

As the SE is an indication of the accuracy of sample mean as compared with the population mean. The smaller it is, the less spreading of data and more likely it is. So, the smaller value of standard error is a good thing.

How do I calculate standard error in Excel?

For the calculations in the excel, you can simply use the following function.
=STDEV (Sampling Range) / SQRT(COUNT(sampling range))

How do you read standard error (SE) bars?

SE bars can tell how the data is spread around the mean value. Smaller the SD bar lowers the suspension, larger SD bar larger suspension of data around the mean.

What does a SE of 2 mean?

As we know from the empirical rule, the 95% values fall in the range of 2 standard errors and approximately 99.7% of means will be in the range of 3 standard errors of the mean.

Why is the standard error important?

It is very important because it tells the fluctuation of the sample in statistics. The standard error helps in the construction of confidence intervals & significance testing, so it is really helpful.

End-Note:

Thankfully, you come to know about the standard error, its applications including; hypothesis testing, confidence interval of the sample and many others in the Statistics. Simply, use this online standard error calculator that helps you to determine the reliability of the sample data. Typically, students & education experts use this online tool to solve their education related problems.

References:

From the source Wikipedia: Standard error of the mean, Student approximation when σ value is unknown and all other statistical approaches.