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Chapter 12: Problem 50

Find the arithmetic mean for each collection of numbers. $$ 2,1,4,8,3,7,10,8,0 $$

Short Answer

Expert verified
The arithmetic mean is 4.78.

Step by step solution

01

- Understand the Arithmetic Mean

The arithmetic mean (or average) of a set of numbers is found by adding all the numbers together, then dividing by the count of numbers.
02

- Add the Numbers

Add all the given numbers:\(2 + 1 + 4 + 8 + 3 + 7 + 10 + 8 + 0 = 43\)
03

- Count the Numbers

Count how many numbers there are in the set:\(2, 1, 4, 8, 3, 7, 10, 8, 0\) contains 9 numbers.
04

- Divide the Sum by the Count

Divide the sum of the numbers by the count of the numbers:\(\frac{43}{9} = 4.78\)

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Key Concepts

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

average of a set of numbers
When dealing with a collection of numerical data, it鈥檚 essential to know how to find the 'average' or 'arithmetic mean'. This value represents a central point of the data set and is widely used in various real-life scenarios like calculating grades, understanding statistics in sports, and many more.

To find the average, you need to follow a simple process:
  • Add all the numbers in the set together.
  • Count how many numbers there are.
  • Divide the sum by the count.
By following these steps, you obtain the arithmetic mean. For example, in the given exercise, the numbers are: \(2, 1, 4, 8, 3, 7, 10, 8, 0\). Adding these gives 43. There are 9 numbers in total, so the arithmetic mean is \( \frac{43}{9} = 4.78 \).
step-by-step arithmetic
Understanding arithmetic operations step-by-step helps in accurately solving problems. Let's break down the process of calculating the arithmetic mean with the given set of numbers: \(2, 1, 4, 8, 3, 7, 10, 8, 0\).

  • Step 1: Add the Numbers: Add all the numbers in the set together: \(2 + 1 + 4 + 8 + 3 + 7 + 10 + 8 + 0 = 43\).
  • Step 2: Count the Numbers: Determine how many numbers are in the set. Here, there are 9 numbers.
  • Step 3: Divide the Sum by the Count: Divide the total sum by the number of elements: \( \frac{43}{9} = 4.78 \).
Each step ensures you reach the correct result efficiently.
basic arithmetic operations
Basic arithmetic operations form the foundation of mathematics. These are the building blocks for solving more complex problems. For calculating the arithmetic mean, we primarily use: Addition and Division.

  • Addition: This operation combines multiple numbers into a single sum. In our example, summing up \(2, 1, 4, 8, 3, 7, 10, 8, 0\) results in 43.
  • Division: This operation distributes the sum evenly across the count of numbers. Dividing the sum 43 by the count 9, we get \( \frac{43}{9} = 4.78 \).
Mastering these operations is key to understanding and performing well in various mathematical tasks.

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