The arithmetic mean of a sequence is found by summing all the values in the sequence and then dividing by the total number of values.
Understanding the Arithmetic Mean
The arithmetic mean, commonly known as the average, represents a central value of a set of numbers. It's a fundamental concept in statistics and is used extensively in various fields.
Steps to Calculate the Arithmetic Mean
- Sum the values: Add all the numbers in the sequence together. If your sequence is a, b, c, d, and so on, calculate a + b + c + d + ....
- Count the values: Determine how many numbers are in the sequence. Let's call this number "n".
- Divide the sum by the count: Divide the sum obtained in step 1 by the number obtained in step 2. This gives you the arithmetic mean.
Formula
The formula for calculating the arithmetic mean is:
Arithmetic Mean = (Sum of all values) / (Number of values)
Example
Let's say you have the sequence: 2, 4, 6, 8, 10.
- Sum the values: 2 + 4 + 6 + 8 + 10 = 30
- Count the values: There are 5 values in the sequence. So, n = 5.
- Divide the sum by the count: 30 / 5 = 6
Therefore, the arithmetic mean of the sequence 2, 4, 6, 8, 10 is 6.
Table Summary
| Step | Description | Example (Sequence: 2, 4, 6, 8, 10) |
|---|---|---|
| 1. Sum Values | Add all the numbers in the sequence. | 2 + 4 + 6 + 8 + 10 = 30 |
| 2. Count | Determine the number of values in the sequence. | 5 |
| 3. Divide | Divide the sum by the count. | 30 / 5 = 6 |
Practical Insights
- The arithmetic mean is sensitive to outliers (extreme values). A single very large or very small number can significantly affect the mean.
- The arithmetic mean is best used when the data is roughly symmetrical (e.g., a normal distribution).
