Problem 142 - Beginning and Intermediate Algebra

Question

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. Work Exercises 139-142 in order, to find the average of \(23,18,13,-4,\) and -8 What is the average of the given group of numbers?

Step-by-Step Solution

Answer

The average is 8.4.

Step 1 - Add All the Numbers

First, add the given numbers together: \(23 + 18 + 13 + (-4) + (-8)\).

Step 2 - Simplify the Sum

Now, simplify the sum of the numbers: \(23 + 18 + 13 - 4 - 8 = 42\).

Step 3 - Count the Terms

Count the number of terms in the group. There are 5 numbers in the group: 23, 18, 13, -4, and -8.

Step 4 - Divide the Sum by the Number of Terms

Divide the sum by the number of terms to find the average: \(\frac{42}{5} = 8.4\).

Key Concepts

mean calculation

The mean, also known as the average, is a measure that represents the central value of a set of numbers. It's used to summarize data with a single value that provides a general idea of the 'middle' of the dataset.
To find the mean, you add up all the numbers in the dataset and then divide the total by the number of values.
This process is valuable in everyday life and various fields, such as statistics, economics, and even sports analytics.

sum of numbers

The first step in calculating the mean is to determine the sum of the numbers. This involves adding all the individual numbers together.
For example, let’s consider the numbers: 23, 18, 13, -4, and -8.
When you sum these numbers, the calculation looks like this:

• Start with the first number: 23
• Add the second number: 23 + 18 = 41
• Add the third number: 41 + 13 = 54
• Subtract the fourth number (since it's negative): 54 - 4 = 50
• Subtract the fifth number (also negative): 50 - 8 = 42

The result of summing these numbers is 42.
This sum is crucial, as it will be used in the next step to calculate the mean.

division in mathematics

The final step in finding the mean involves division. Here, you divide the sum of the numbers by the number of terms in the dataset.
Using our previous example, we have a sum of 42 and 5 numbers (23, 18, 13, -4, -8) in the group.
To find the mean, perform the division:
\[\frac{42}{5} = 8.4\]
This gives us a mean value of 8.4. This value represents the average, or central value, of our original set of numbers.
Division in this context helps distribute the total sum evenly across the number of terms, providing a clear and balanced measure of the data set.