Problem 144 - Beginning and Intermediate Algebra

Question

Find the average of each group of numbers. -17,34,9,-2

Step-by-Step Solution

Answer

The average is 6.

Step 1 - Sum the Numbers

First, add all the numbers together. \[ -17 + 34 + 9 + (-2) \]Calculate this sum: \[ -17 + 34 = 17 \] \[ 17 + 9 = 26 \] \[ 26 + (-2) = 24 \]

Step 2 - Count the Numbers

Now, count how many numbers are in the set. The numbers given are: -17, 34, 9, -2. So, there are 4 numbers.

Step 3 - Divide the Sum by the Count

Finally, divide the sum from Step 1 by the count from Step 2. \[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Total count}} \]\[ \text{Average} = \frac{24}{4} = 6 \]

Key Concepts

Sum of Numbers

To find the average, the first step is to calculate the sum of all the given numbers. In this case, we have the numbers -17, 34, 9, and -2.

The sum is calculated by adding these numbers together: \br>
\( -17 + 34 + 9 + (-2) \).
You can break the addition into smaller steps for simplicity: \br>

\
• First, adding -17 and 34: \( -17 + 34 = 17 \)\
• Next, add 17 to 9: \( 17 + 9 = 26 \) \
• Finally, add 26 and -2: \( 26 + (-2) = 24 \).\

Therefore, the sum of the given numbers is 24.

Counting Numbers

The next step is to count how many numbers are in the set. This is crucial because the average is found by dividing the sum by this count.

Looking at our example, the list of numbers is: -17, 34, 9, and -2.

To find the count, simply determine how many numbers are listed. This set contains 4 numbers.

Always double-check the count to ensure accuracy. Incorrectly counting the numbers can lead to wrong results in the final step.

Average Calculation

Once you have the sum and the count, finding the average is straightforward.

The formula for calculating the average is: \
\ \[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Total count}} \]

Using our calculated values: \br> \br> Sum = 24, Count = 4 \br> \br> Plug these into the formula: \ \br> \[ \text{Average} = \frac{24}{4} = 6 \].

So, the average of the numbers -17, 34, 9, and -2 is 6.

Always remember, the average helps in understanding the central tendency or the mean value of a set of numbers.