# Sample Mean Calculator

## Sample Mean Calculator

### Related Tools

Sample has 28 observations.
Sample Mean: 5.1429

## How to Use a Sample Mean Calculator and Interpret a Sample Mean

This is a simplified version of our descriptive statistics tool which calculates just the sample mean. It is intended for students and others who are looking for just this statistic.

The sample mean is a common statistic which is calculated as the sum of the observations divided by the number of observations in the sample. This is also commonly referred to as the average of a set of observations.

In statistical terms, the sample mean can be viewed as an estimator of the overall population mean of the population from which it was drawn. It is one of the most commonly used measures of the location (aka the center) of a statistical distribution. It should be noted that the sample mean is not necessarily regarded as a robust statistic. The value of a sample mean is highly sensitive to outliers, extreme values of the distribution which can distort the average. This is especially common if the underlying distribution is not normal, such as an exponential or power-law distribution. Along the same lines, the mean is not necessarily representative of measurements of quality and customer satisfaction. For example, while a regression model might show that ice cream is best when stored in a freezer kept at an average of 25 degrees, common sense would indicate not to expect a good result if we achieved that average by spending half our time at 50 degrees and the balance at zero degrees. We would have a melted mess! The same challenge exists in financial and risk management applications: a borrower's average balance is less important than the chance they will out of money on the specific day we need payment!

This tool is developed so you can save your data and use it in our other calculators. Simply hit "save data" and enter a name for this data set. It will be added to the menu shown alongside (or below) the calculators. When you open another page on our site, you will see a list of saved datasets. Simply click on that item and it will pre-populate the calculator box.

A sample mean calculator is a tool that calculates the average of a set of observations in a sample. It is a commonly used measure of the location or center of a statistical distribution. The sample mean is used as an estimator of the overall population mean of the population from which it was drawn.

## Using a Sample Mean Calculator

To use a sample mean calculator, you need to input the set of observations from your sample. The calculator will then calculate the sample mean by summing up all the observations and dividing by the number of observations in the sample.

For example, if you have a sample of 10 observations with values of 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20, the sample mean calculator will calculate the sample mean as follows:

(2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20) / 10 = 10

Therefore, the sample mean for this sample is 10.

## Interpreting a Sample Mean

The sample mean provides an estimate of the population mean based on the sample data. However, it is important to note that the sample mean is not necessarily a robust statistic. The value of a sample mean is highly sensitive to outliers, which are extreme values of the distribution that can distort the average.

For example, if you have a sample of 10 observations with values of 2, 4, 6, 8, 10, 12, 14, 16, 18, and 200, the sample mean will be greatly influenced by the outlier value of 200. In this case, the sample mean will be:

(2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 200) / 10 = 28.8

Therefore, the sample mean for this sample is 28.8, which is greatly influenced by the outlier value of 200. In this case, the sample mean is not a good estimator of the population mean because it is greatly distorted by the outlier value.

Another important consideration when interpreting a sample mean is the sample size. As the sample size increases, the sample mean becomes a more reliable estimator of the population mean. This is because larger sample sizes provide more information about the underlying population distribution and reduce the effect of random variation in the sample.

Additionally, the standard deviation of the sample is an important factor to consider when interpreting the sample mean. The standard deviation provides a measure of the spread of the data around the mean. A large standard deviation indicates that the data is widely spread out, while a small standard deviation indicates that the data is tightly clustered around the mean.

## Conclusion

A sample mean calculator is a useful tool for calculating the average of a set of observations in a sample. However, it is important to interpret the sample mean in the context of the sample size, the standard deviation, and the presence of outliers. A larger sample size and a smaller standard deviation will result in a more reliable estimate of the population mean, while the presence of outliers can greatly distort the sample mean. By understanding how to use a sample mean calculator and how to interpret a sample mean, you can make more informed decisions based on your sample data.