# How to Calculate Standard Error (Using a Formula)

Standard error is a statistical measure that quantifies the variability of a sample mean from the population mean.

It helps you understand the precision of sample-based results and facilitates informed decisions. And the best part, it is not even difficult to calculate 🧮

If you’re also up to enhancing the rigor of your statistical calculations, make sure you get your hand on your free practice workbook for this guide here and read along with me till the end.

## What is Standard Error

The standard error is a measure of variability across samples.

Bringing it down to simpler words, the standard error tells how to measure the variability between a sample mean and a population mean.

A higher standard error shows that the sample is widely spread and is not a true representation of the population. A low standard error shows vice versa 📨

By calculating the standard error, you can estimate how well your drawn sample represents the total population and draw valid conclusions accordingly.

## Formula

The formula of Standard Error is:

Click to copy

In words:

Click to copy

The calculation begins with calculating the Standard Deviation of the sample mean and then dividing it by the square root of the number of items in the sample.

## Why is Standard Error important

Calculating standard error is important as it helps you draw true conclusions about a population based on a sample drawn from it by estimating how well that sample represents the population.

For example, if you want to calculate the average height of men in a town. It will not be possible for you to get the height of every man in that town. We will instead draw a sample of men (including men of all age groups and weight etc.) and conclude it 📝

However, the sample we select might not be an actual representation of the entire population. It might not cover all aspects of the population. Accordingly, the mean we calculate for the sample may be around 5.7 feet (just an exemplary number).

However, if you had taken the entire population, the actual population mean might have been 6.3 feet. The higher the difference between these means, the higher the standard error.

To know how accurately a selected sample represents the underlying population and to what extent can we place reliance on it, we need to calculate the standard error.

### Pro Tip!

A greater standard error represents sampling bias. It tells that the sample doesn’t give a true picture of the entire population. Also, that there is greater dispersion in population.

To help with sampling bias, you can reconsider the sampling technique employed by you (random sampling, haphazard sampling, block sampling, etc.) and increase the sample size.

As the sample size increases, more portion of the population is covered, and the sampling bias is reduced.

## Calculating Standard Error in Excel

Guess we have had enough talk on what standard error is, how is it important, and so on.

But the most important question remains unanswered – how do you calculate it?

Calculating Standard Error in Excel is far easier than doing it manually since we have built-in MS Excel functions to calculate the components of the Standard Error formula 💻

Ready to see how it’s done? Let’s begin.

Here I have a sample of the heights of men from Town XYZ.

The entire population would consist of hundreds of men living across the town. So we have drawn a sample of heights of men of different attributes.

To calculate the standard error for these heights:

Step 1) Write the STDEV.S function as follows:

Click to copy

Excel offers multiple standard deviation functions including STDEV.P which is meant to calculate the standard deviation for a population. Since we are dealing with a sample dataset, we will use the STDEV.S function.

Step 2) Refer to the cell range that contains the sample data to calculate the standard deviation of the same.

Click to copy

We have the standard deviation of the sample dataset calculated as 0.432.

Step 3) Calculate the number of items in the sample by using the COUNT function as follows:

Click to copy

This gives us the sample size (the n from the standard error formula).

Step 4) Calculate the square root of this number by using the SQRT function as below.

Click to copy

Cool – now we have all our data points ready.

Step 5) To calculate the standard error value, divide the standard deviation of the sample by the square root of n like below.

Click to copy

And there you have it – 0.15.

If you have now understood the standard error calculation dynamics, you can save time by automating this entire calculation in one formula and step as shown below ⏭

Click to copy

Microsoft Excel makes the calculation of standard error considerably easy and quick.

## Interpreting Standard Error

After you have calculated the standard error for a given sample dataset, the next most important step is to interpret it 💭

What does a standard error of 0.15 mean?

To understand this, we first need to calculate the mean of the sample dataset before us.

Step 1) Use the AVERAGE function to find the mean for this sample dataset.

Click to copy

The mean of the sample of men’s heights comes out as 5.76 feet.

To accurately express it we will say the mean of height of men from town XYZ is 5.76 +- 15 feet.

This tells that based on the standard error calculation, the mean of this sample of heights might be more or less 0.15 feet. That’s how we interpret and report the standard error for a mean together with the sample mean 🙌

### Pro Tip!

A standard error can be reported together with the mean as shown above or as a confidence interval.

A confidence interval expresses a range of values within which you can expect an unusual population item to exist if a new random sample was drawn from the same.

However, reporting the standard error together with the mean is also an appropriate approach as it explains the range of variation users can expect in the population mean.

## Conclusion

Drawing a sample from a population and drawing conclusions based on the same is something you’d see everywhere around the world.

The above guide is curated to help you master the calculation of standard error in Excel since it equips you with a powerful tool to assess the precision of sampling statistics. And resultantly, you’re able to draw sound conclusions from it about the whole population.

Standard error is a key statistical measure that ensures the validity and robustness of sample-based statistical outcomes. Knowing more about similar statistical measures will be of better help – hop on to my following Excel tutorials to learn these.