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Chapter 1: Problem 55

Find the average of \(\$ 64, \$ 97,\) and \(\$ 121\).

Short Answer

Expert verified
The average is \(94 \) dollars.

Step by step solution

01

- Sum of the numbers

First, find the sum of the given numbers: \(64 \) dollars, \(97 \) dollars, and \(121 \) dollars. So, add them together: \[64 + 97 + 121 = 282 \] dollars.
02

- Count the numbers

Count the total number of values. In this case, there are three numbers: \(64 \) dollars, \(97 \) dollars, and \(121 \) dollars.
03

- Calculate the average

To find the average, divide the sum from Step 1 by the count from Step 2: \[ \frac{282}{3} = 94 \] dollars.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

sum of numbers
When we are given a list of numbers and asked to find the average, the first step is always to find the sum of these numbers. Summing or adding up these values gives us a single total. For instance, in our exercise, we need to find the sum of \(64 dollars, 97 dollars, \) and \(121 dollars.\) Here鈥檚 how you do it:
\[64 + 97 + 121 = 282 \] dollars.
We add each number one by one until we reach the total: 282 dollars. Summing helps us collect all individual values into one, making it easier to calculate the average.
count of values
The second step in finding an average is determining the total count of values. It's important to check how many numbers we are working with. In our case, we have three numbers: \(64 dollars, 97 dollars, \) and \(121 dollars.\) Therefore, the count of values is 3. Counting the numbers helps us understand how many individual values contribute to our sum, which we need for accurate averaging.
average formula
Finally, we calculate the average. The average (or mean) is found by dividing the sum of all numbers by the count of those numbers. This formula looks like this:
\[ \text{Average} = \frac{\text{Sum of values}}{\text{Count of values}} \]
In our exercise, we already know the sum (282 dollars) and the count (3). Plugging these into our formula, we get:
\[ \frac{282}{3} = 94 \] dollars. Thus, the average of \(64 dollars, 97 dollars, \) and \(121 dollars \) is \(94 dollars\). The average gives us a single number that represents all the values, making it easier to understand and compare.

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