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Chapter 12: Problem 49

Find the arithmetic mean for each collection of numbers. $$ 5,9,8,2,4,7,3,2,0 $$

Short Answer

Expert verified
The arithmetic mean is approximately 4.44.

Step by step solution

01

- Understand the Problem

The goal is to find the arithmetic mean of the given set of numbers: 5, 9, 8, 2, 4, 7, 3, 2, 0.
02

- Sum of the Numbers

Add all the numbers together. \[ 5 + 9 + 8 + 2 + 4 + 7 + 3 + 2 + 0 = 40 \]
03

- Count the Numbers

Determine how many numbers are in the set. There are 9 numbers in total.
04

- Calculate the Arithmetic Mean

Divide the sum of the numbers by the amount of numbers. \[ \text{Mean} = \frac{40}{9} \approx 4.44 \]

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Key Concepts

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

mean calculation
Calculating the arithmetic mean might sound complicated, but it's actually very simple. The arithmetic mean is also known as the average. It's a way to find the central value of a group of numbers. To find the mean, you need to perform two main operations: addition and division. This process helps to understand what is normal or typical for a set of numbers. For example, if you have the numbers 5, 9, 8, 2, 4, 7, 3, 2, 0, the steps for calculating the mean will involve adding all these numbers first and then dividing by how many numbers there are.
sum of numbers
The first essential step in calculating the arithmetic mean is to find the sum of the numbers. Adding numbers might seem basic, but it is crucial for getting the right mean. For the set of numbers: 5, 9, 8, 2, 4, 7, 3, 2, 0, you will add them like this:
\[ 5 + 9 + 8 + 2 + 4 + 7 + 3 + 2 + 0 = 40 \]
Addition involves combining the total value of all the numbers in the set. Each number contributes to this sum, giving a collective worth that will be further used in our calculation.
counting numbers
Once you've summed up all the numbers, the next step is to count how many numbers there are. This step is important because understanding the size of your data set ensures you calculate the mean correctly. In our example with numbers: 5, 9, 8, 2, 4, 7, 3, 2, 0, you simply count each number to see that there are 9 numbers in total. Knowing the total count helps us to proceed to the next step of dividing this sum.
division
The final step in finding the arithmetic mean is the division. After adding all the numbers (which in our example is 40), and understanding that there are 9 numbers in total, you divide the sum by the count. This step spreads the total value equally among all numbers, finding the central point.
The formula looks like this:
\[ \text{Mean} = \frac{40}{9} \]
Carrying out this division gives us approximately 4.44. This final value is what we call the arithmetic mean or average. It summarizes our data into one representative number.

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