Descriptive Statistics

Arithmetic Mean Calculator

Use this calculator to find the arithmetic mean, A, for a set of data values. Enter your values and click Calculate to get instant result with a clear step-by-step solution.

How to Use the Arithmetic Mean Calculator

This calculator allows you to quickly find the arithmetic mean of a set of data values. To use the calculator:

Enter the data values in the data input field. You should separate them using commas, spaces, tabs, or line breaks. Alternatively, you can copy-paste values directly from Excel, Google Sheets, or even text documents.
Click Calculate

The calculator will instantly return the arithmetic mean (A) and show you exactly how the value was obtained, using a step-by-step approach.

This tool is only appropriate when the data values contribute equally to the final mean. Therefore, if each data value has a unique weight that contributes to the final average, use the weighted average calculator. However, if you’re working with grouped data with class intervals and frequencies, the grouped mean calculator might be useful.

What Is Arithmetic Mean?

The arithmetic mean is the ordinary average of a set of numbers. Thus, you can simply find the arithmetic mean by adding all values and dividing the result by the number of observations.

In many basic statistics problems, the words mean, average, and arithmetic mean are used interchangeably. However, the term arithmetic mean is more precise because it tells us the exact type of mean being used. This matters because the arithmetic mean is only one type of mean. Other types include the geometric mean, harmonic mean, and weighted mean. These are calculated differently and are useful in different situations.

Arithmetic Mean Formula

The arithmetic mean formula is:

Where:

A is the arithmetic mean
∑xi is the sum of all observations
n is the total number of observations

Sometimes, the formula is written in its expanded form as follows:

Arithmetic mean = (x₁ + x₂ + … + x_n) / n

where:

x₁, x₂, …, x_n are the individual values in the dataset.
n is the total number of observations in the dataset.

Therefore, we find the arithmetic mean by summing all the values in the dataset and dividing the result by the total number of observations.

How to Find the Arithmetic Mean

To find the arithmetic mean manually:

Add all the data values.
Count the number of observations to get n.
Divide the sum of all values by n

Example

A researcher records the following waiting times, in minutes, for 8 customers: 4, 6, 5, 8, 7, 9, 6, 3. Find the arithmetic mean waiting time.

Solution

To find the arithmetic mean for the dataset by hand, follow these steps.

Step 1: Add all the data values.

The sum of all values in the dataset is: 4 + 6 + 5 + 8 + 7 + 9 + 6 + 3

= 48

Step 2: Count the number of observations.

There are 8 values in the dataset. Thus, n = 8

Step 3: Divide the sum of all values by n

By definition, the arithmetic mean formula is: A = ∑xi /n

Substituting the values, we get:

A = 48/8

= 6

Therefore, the arithmetic mean is x̄ = 6. This means that the average waiting time is 6 minutes.

Want to verify the results using the arithmetic mean calculator? Follow these steps:

Copy and paste the values in the data input field
Click calculate

The calculator will yield similar results and also show you how the value was obtained.

Arithmetic Mean vs Average

In many everyday situations, arithmetic mean and average mean the same thing. For example, if someone asks for the average of 10, 20, and 30, they usually want the arithmetic mean, which can be computed as follows:

(10 + 20 + 30)/3

= 20

Thus, the average is 20.

However, the word average can be broad. It may refer to the mean, median, mode, or another measure of central tendency depending on the context. The arithmetic mean is more specific because it refers to the value found by adding all observations and dividing by the number of observations.

Therefore, if you simply want a quick everyday average, use the average calculator. However, if you want the formal arithmetic mean as a type of mean, this calculator is the better fit.

Want a tool that distinguishes sample mean from population mean with proper symbols? Use the mean calculator.

Frequently Asked Questions

What is an arithmetic mean calculator?

This is an online tool that finds the arithmetic mean of a set of numbers. It adds all values and divides the result by the number of values.

What is the arithmetic mean formula?

The formula is $A = \frac{1}{n}\sum_{i=1}^{n} a_i$ , where A is the arithmetic mean, n is the number of values, and a_i represents each value in the dataset.

How do you calculate the arithmetic mean?

To calculate the arithmetic mean, add all values in the dataset, count the number of values, and divide the sum by the count.

Is arithmetic mean the same as average?

In most everyday situations, yes. The arithmetic mean is the usual average found by adding values and dividing by the number of values. However, in statistics, arithmetic mean is more specific because there are other types of means.

Why is the arithmetic mean affected by outliers?

The arithmetic mean uses every value in the dataset. As such, a very large or very small value can pull the mean upward or downward.