Problem 143 - Beginning and Intermediate Algebra

Question

Find the average of each group of numbers. -15,29,8,-6

Step-by-Step Solution

Answer

The average is 4.

Step 1 - Sum the Numbers

Add all the given numbers together: -15 + 29 + 8 + (-6)

Step 2 - Calculate the Total Sum

Perform the addition from Step 1: -15 + 29 = 14 14 + 8 = 22 22 + (-6) = 16

Step 3 - Count the Numbers

Count the total number of values in the set: There are four numbers: -15, 29, 8, -6

Step 4 - Compute the Average

Divide the total sum by the number of values: The average is given by \[ \text{Average} = \frac{\text{Total Sum}}{\text{Number of Values}} = \frac{16}{4} = 4 \]

Key Concepts

Sum of Numbers

To find the average of a set of numbers, the first step is to calculate their sum. Imagine you have a group of numbers, for example, -15, 29, 8, and -6. The objective is to add these numbers together.
In arithmetic, summing numbers requires dealing with both positive and negative values correctly. For our example:
1. Add -15 and 29, which gives 14
2. Add the result, 14, to 8, which equals 22
3. Add 22 to -6, resulting in 16

Thus, the total sum of the numbers -15, 29, 8, and -6 is 16. Summing numbers is a foundational skill that applies to various mathematical problems.

Counting Values

Once you have the total sum, the next step is to count how many numbers you have added. This is crucial because the average is determined by dividing the total sum by the count of numbers.
In our example, we need to count the numbers: -15, 29, 8, and -6.
There are 4 numbers in this set.
Counting values accurately ensures that you compute the average correctly. It's a simple but essential part of solving these kinds of problems.
Remember:

• Counting helps in measuring quantity.
• It is vital for steps involving further division and proportions.
• Mistakes in counting lead to errors in finding the average or other calculations.

Division in Arithmetic

After summing the numbers and counting how many numbers there are, the final step is to compute the average. This involves division. For our example:

• Total sum of numbers = 16
• Number of values = 4
• Average = Total sum / Number of values

The formula to find the average is:
\[\text{Average} = \frac{\text{Total Sum}}{\text{Number of Values}}\]Plugging the values into the formula, we get:
\(\frac{16}{4} = 4\)
Therefore, the average of -15, 29, 8, and -6 is 4. Division helps distribute a total amount equally. Understanding division ensures precise results, especially in problems involving averages.