Problem 140 - 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 How many numbers are in the group?

Step-by-Step Solution

Answer

5 numbers, average is 8.4.

Step 1 - Count the Numbers

First, determine how many numbers are in the group. Here, the numbers given are 23, 18, 13, -4, and -8. Count these numbers.

Step 2 - Add the Numbers

Next, we need to find the sum of the numbers. Add 23, 18, 13, -4, and -8: \(23 + 18 = 41\) \(41 + 13 = 54\) \(54 - 4 = 50$$50 - 8 = 42\). Hence, the sum is 42.

Step 3 - Divide the Sum

The sum of the numbers is 42, and there are 5 numbers in the group. To find the average, divide the sum by the number of terms: \(\frac{42}{5}\).

Step 4 - Simplify the Result

Divide 42 by 5 to get the average: \(\frac{42}{5} = 8.4\). So, the average of the given numbers is 8.4.

Key Concepts

arithmetical mean

The arithmetical mean, or simply the mean, is a measure of central tendency. It gives us an idea of the average value of a set of numbers.
The mean is very useful in various fields like statistics, economics, and everyday life.
Essentially, it tells us what a typical value in the set might be.
To calculate the mean, follow these simple steps:

• Add up all the numbers in your set to get the sum.
• Count how many numbers are in the set.
• Divide the sum by the number of numbers.

By doing this, you get the average, which is the arithmetical mean of your numbers.

sum of numbers

The sum of numbers is the result of adding all the numbers in a group together. In our example, we have the numbers 23, 18, 13, -4, and -8.
Here's how you add them step by step:
First, add 23 and 18 to get 41.
Then, add 13 to 41, giving you 54.
Next, subtract 4 from 54, which results in 50.
Finally, subtract 8 from 50, and you'll have 42.

• This sum is crucial because it is used in calculating the mean.
• Without finding the correct sum, your mean could be incorrect.

division

Division is one of the four basic operations in arithmetic. It is the process of determining how many times one number is contained within another.
In the context of finding the mean, division is used to distribute the sum of the numbers equally among the number of terms.
In our example, the sum of the numbers is 42, and there are 5 numbers.
To find the mean, we divide 42 by 5: \[\frac{42}{5} = 8.4\]
This division shows that, on average, each number in the set is 8.4.