Standard Error Calculator

Our standard error calculator calculates the standard error of the mean or grouped data for a given set of data by using standard deviation and sample size.

What is Standard Error?

“An assessment of the statistical accuracy, which signifies the standard deviation in the theoretical distribution over a considerable population”.

• A smaller value of standard error shows the statistic is more likely to be close to the population value. 
• A larger value of standard error represents that the statistic is less likely to be close to the population value.

Standard Error Formula:

The standard error of a statistic is a measure of the accuracy. When you want to eliminate the errors then our standard error calculator comes into play. It determines the standard error of the mean for your specified numerical values.
 
$$ SE = \frac{s}{\sqrt{n}} $$

Where:

• SE = Standard error of the mean 
• s = Standard deviation 
• n = Number of samples 

How To Calculate Standard Error of The Mean?

The standard error is used to measure how reliable a sample statistic is close to the population value. It is determined by dividing the sample standard deviation by the square root of the sample size.

Our standard error calculator calculates the standard error by using the standard deviation and sample size and provides an exact measure of data dispersion within a group or sample.

Practical Example: 

Assume, you have a sample of 100 students and you figure out the average height of a student to be 5 feet and 6 inches with a standard deviation of 3 inches. What is the standard error of the mean height?

Solution:

Given Data:

Standard Deviation = 3
Sample Size = 100

Standard Error Equation:

The standard error of the mean formula helps you to understand how to find standard error.

$$ SE = \frac{s}{\sqrt{n}} $$

Find The Standard Error:

SE = 3 / √ 100

SE = 3 / 10

SE = 0.3

This means that you can be 95% confident that the average height of all students in the population is between 5 feet 5.7 inches and 5 feet 6.3 inches. Providing the following values is required to make it work!

How Standard Error Calculator Work?

Our standard error of the mean calculator is developed to determine insights into the precision of sample data because it is considered the key to producing the confidence interval.

What To Enter?

• First, select the raw data or summary data
• For raw data, only insert the set of data 
• For summary data, write the value of standard deviation and the sample size 

What To Get?

Our standard error calculator will show you the below terms by considering the above values.

• Standard error of numbers 
• Mean value 
• Standard deviation 
• Step-by-step calculations 

Frequently Asked Questions:

What Is The Sample Size?

The number of observations that are used to evaluate the sample statistics is known as sample size. It is always inversely proportional to the standard error.

What Is Confidence Interval?

It is the range of values that contains the population mean. The wider the confidence interval, the less confident you can be that the statistic is close to the population value.

What Is a Good Standard Error Value?

A good standard error means that it is relatively smaller than the mean of statistics. If the standard error is smaller then it means, statistics is likely to be close to the population value. 

Citations:

Wikipedia: Standard error, Standard error of the sample mean, Student approximation when σ value is unknown, Assumptions and usage. 

Investopedia: What Is the Standard Error? Formula and Calculation of Standard Error, Requirements for Standard Error, Standard Error vs. Standard Deviation, Example of Standard Error, What Is a Good Standard Error?

Scribbr: Why standard error matters, Standard error vs standard deviation, Standard error formula, How should you report the standard error?