Understanding the Arithmetic Mean

What is the Arithmetic Mean?

The arithmetic mean, often simply called the average, is a central value of a set of numbers. It's calculated by adding up all the numbers and then dividing by how many numbers there are.

Formula and Its Components

The formula for the arithmetic mean is:

\[\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}\]

Where:

• \(\bar{x}\) is the arithmetic mean
• \(\sum\) means "sum of"
• \(x_i\) represents each individual value in a dataset
• \(n\) is the total number of values

Calculation Steps

1. Add up all the numbers in your dataset.
2. Count how many numbers you have.
3. Divide the sum by the count.

Example Calculation

Let's calculate the arithmetic mean for the dataset: 2, 4, 6, 8, 10

1. Sum the numbers: \(2 + 4 + 6 + 8 + 10 = 30\)
2. Count the numbers: There are 5 numbers
3. Divide: \(\frac{30}{5} = 6\)

Therefore, the arithmetic mean is 6.

Visual Representation

This scatter plot represents our example dataset. Each blue dot is a data point, and the red dashed line shows the arithmetic mean (6).