standard error of mean

What is Standard Error? Know About It Today

Today, we will be discussing one of the common mathematical terms that is used very much in modern mathematics. The name of the term is Standard Error of Mean. It is primarily used to measure variability. Using the Standard Error, we can have an estimation regarding the sample’s standard deviation.

Using Standard Error, one can obtain the accuracy as well as the consistency and efficiency of a sample. Using it, we can understand how accurately a sampling distribution is related to the population.  

The application of Standard Error is wide. It can use in statistics as well in economics. Researchers who involve in the calculation of regression as well as perform the hypothesis testing also use them in great amounts. Inferential statistics is also one place where Standard Error is used. Following are various terms that co-relate with Standard Error.  

  •       The Median of standard error
  •       Standard error of the regression coefficient
  •       Standard error of Mean. The standard error of mean is generally denoted by SEM.
  •       A variance of Standard error.

Now, we will be going to look at the Standard error of the Mean. (SEM)

Standard Error of Mean Formula

Below shown is the Standard error formula.


Here, x represents the Standard Deviation of the population while n represents the size of the sample. It generally coins as the number of observations conducted in the sample. 

There is another formula through which the calculation also does. This formula uses when the population standard deviation can ignore. In place of it, the sample standard deviation can take into consideration. Note that this formula can only apply when the samples known to us exist as statistically independent. 


Here, n represents the size of the sample. It generally coins as the number of observations conducted in the sample. Meanwhile, s represents the Standard Deviation of the sample. 

How important Standard Error of Mean is?

standard error of mean


At the point when an example of various observations extract from a population and the sample mean to determine, it fills in as a gauge of the population mean. Generally, the Sample mean that has been calculated might vary from the actual mean of the population.

It will help the analyst’s examination to recognize the degree of variation that has been caused. It is the place where the standard error of the mean becomes an integral factor. 

There might be the existence of a case in which multiple samples retract from the population, in such case, the standard error of the mean is the standard deviation of various means of the sample from the population mean. 

In any case, numerous examples may not generally be accessible to the analyst. Luckily, the standard error of the mean is widely available and can be determined from a solitary example itself.

The method to calculate the same is as follows. The standard deviation of the various observations of the sample is divided by the square root of the size of the sample. 

Also Read: What is the Law of Large Numbers? (Brief Explanation)

What Is the Relationship Between Sem and the Size of the Sample?

standard error of mean


In general times, it is quite evident that as the size of the sample increases, it represents more amount of substance from the population. This way, it becomes closer and closer to the actual reality of the population. 

Let us take an example that will make you understand the concept with ease. Consider the scenario of 100 students that are taking part in a school examination. In this examination, let us take our sample from the students. In Sample A, we will pick 20 students randomly and in sample B, we will pick 70 students from the group of students. 

Sample B will be more precise for the calculation of the average marks of the student as it has a greater number of students inside it. That means that the standard error of the mean of Sample A will be high compared to B.

There will be less chance of error to occur in sample B compared to sample A. For ideal cases, the sampling error will tend to move towards zero, if the number of participants or the observations is increasing. More the number of observations, the less the standard error percentage.

Also, from the formula, we can note that the Standard error of the mean is inversely proportional to the size of the sample. Thus, if the sample size increase by 16 times, then it is evident from the formula that the error will decrease 4 times. 

The Conclusion:

This was all about the standard error and standard error of the mean. The standard error is an important concept for research, for analysis as well as for educational purposes of the students. Using Standard error, we can determine the amount of variation that has been caused.

We hope that the article has served its purpose and whenever you need to look for the terms, you can find us right here! For all financial aid and guidance, keep making your way to FinanceShed.