To find the average of integers between two numbers, you add up all the integers in the set and then divide by the total number of integers.
Here's a breakdown of the process:
Calculating the Average of Integers
Calculating the average, also known as the mean, involves two simple steps:
- Sum the Integers: Add all the numbers in your set together.
- Divide by the Count: Divide the total sum by the number of integers you added.
According to the reference:
Add up the integers in total, then divide by the Total amount of numbers you are averaging.
Example:
Let’s say you want to find the average of the integers between 1 and 9, assuming you mean all integers between 1 and 9 inclusive:
- Integers: 1, 2, 3, 4, 5, 6, 7, 8, 9
- Step 1: Sum the integers: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
- Step 2: Count the integers: There are 9 integers.
- Step 3: Divide the sum by the count: 45 / 9 = 5
- Average: The average of the integers between 1 and 9 is 5.
Example from Reference:
The provided reference provides another clear example:
- Numbers: 1, 3, 4, 6, 7, 9
- Sum: 1+3+4+6+7+9 = 30
- Total Count: There are 6 numbers.
- Average: 30 / 6 = 5.
Therefore, the average is 5.
Practical Insights
- Inclusive vs. Exclusive: Be sure to clarify if the problem means inclusive (including the starting and ending integers) or exclusive (not including them) when interpreting "between".
- Large Ranges: For a very large set of sequential integers, you can sometimes use shortcuts. For instance the average of an arithmetic sequence, is simply the average of the first and last terms. For example with 1 to 1000 (1+1000)/2 = 500.5.
| Step | Description | Formula |
|---|---|---|
| 1 | Sum all the integers | Integer1 + Integer2 + ... + Integern |
| 2 | Count the total number of integers | Total Count (n) |
| 3 | Divide the sum by the count | (Sum of Integers) / (Total Count) |
