Sample Mean Calculator

The sample mean is the average of a selected group of numbers. In statistics, you usually have a large population that is too big to measure completely. Instead of measuring every single item or person, you take a smaller group called a sample. The average of this smaller group is the sample mean.

For example, if you want to know the average height of all high school students in a state, you cannot measure everyone. Instead, you measure 100 students. The average height of those 100 students is your sample mean. Statisticians use this number to guess the true average of the whole state.

Finding the sample mean by hand is a simple process. You just need to follow two basic steps.

1. Add all the numbers in your data set together to find the sum.
2. Divide that total sum by the number of values in your set.

The Sample Mean Formula

Mathematicians use a specific formula to write out this process. The sample mean formula is written as x̄ = Σx / n.

Here is what each part of the formula means:

• x̄ is the sample mean. This is pronounced "x bar".
• Σx is the sum of all the data points. The sigma symbol (Σ) means "add up".
• n is the total number of data points. This is also known as your sample size.

Step by Step Example

A cafe counts weekday customers: 142, 167, 155, 181, and 160. Those five days are a sample of a longer month.

1. Add the counts: 142 + 167 + 155 + 181 + 160 = 805.
2. There are 5 days, so n = 5.
3. Divide: 805 / 5 = 161.

The sample mean is 161 customers per weekday. Enter the same five numbers in the calculator above to confirm.

People often confuse the sample mean with the population mean. The difference comes down to the size of the group you are studying.

The sample mean only looks at a small part of a group. The population mean looks at every single member of a group. We use the sample mean to guess the population mean because counting everyone is usually too hard, too expensive, or takes too much time.

They also use different symbols in math. The sample mean uses the symbol x̄. The population mean uses the symbol μ, which is pronounced "mu".

The accuracy of your sample mean depends heavily on how many items are in your sample. If your sample size is very small, your sample mean might be very different from the true population mean. As you add more data points to your sample, your sample mean becomes a much better guess for the population mean. If you are designing a study, you can use our sample size calculator to figure out exactly how many data points you need to get accurate results.

This tool is designed to be fast and easy for students and professionals alike. Results update instantly as you type, so there is no button to press.

1. Choose your data format: a plain list of values, or a frequency table.
2. Type or paste your numbers into the text box. Separate them with commas, spaces, or new lines.
3. Optionally set the confidence level and decimal places under Options.
4. Read the results, which show the sample mean, the sum of your numbers, the total count, and the intermediate steps. Use the Copy button to save them.

Understanding the mean is a great first step before looking at how spread out your data is. Once you find your average, you can use our standard deviation calculator to see how far your numbers range from that average.