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Chapter 14: Problem 56

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

Short Answer

Expert verified
The arithmetic mean is 4.78.

Step by step solution

01

- Sum the Values

Add all the numbers in the set together: \[2 + 1 + 4 + 8 + 3 + 7 + 10 + 8 + 0 = 43\]
02

- Count the Number of Values

Count how many numbers are in the set. There are 9 numbers in this set.
03

- Divide the Sum by the Number of Values

Divide the sum from Step 1 by the count from Step 2: \[\frac{43}{9} = 4.78\]

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Key Concepts

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

Sum of Values
In order to find the arithmetic mean, the first step is to calculate the sum of all the values. The arithmetic mean is a type of average, and finding the sum is crucial.
To do this, you simply add up all the numbers in your data set. Let's take an example set of numbers: 2, 1, 4, 8, 3, 7, 10, 8, 0. When we add these numbers together, we get:
$$2 + 1 + 4 + 8 + 3 + 7 + 10 + 8 + 0 = 43$$
By finding the sum, you are laying down the foundation needed for further calculations.
Ensure that every value in the set is included in the addition to get an accurate sum.
Number of Values
The next important step after finding the sum is to count how many values you have in your set. This is referred to as the 'number of values.'
Counting the number of values is straightforward but extremely important. An incorrect count at this step can lead to the wrong arithmetic mean.
In our example, the set contains 9 numbers: 2, 1, 4, 8, 3, 7, 10, 8, 0. We can count each value to confirm there are 9 numbers.
  • Make sure the count is accurate.
  • This count will be used as the divisor in the next step.
Getting the count right is essential so that you divide the sum by the correct number in the final step.
Division
The final step in finding the arithmetic mean is to divide the sum of the values by the number of values. This will give you the arithmetic mean.
Using our previous results, we have a sum of 43 and a number of values counted to be 9. We divide the sum by the number of values:
\[\frac{43}{9} = 4.78\]
This gives us an arithmetic mean of 4.78 for our set of values. Division is the step that brings everything together, turning the sum and count into a single, meaningful number: the arithmetic mean.
So, remember to carefully perform the division to get an accurate result!

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Most popular questions from this chapter

Solve each applied problem by writing the first few terms of a sequence. Leslie is offered a new job with a salary of \(20,000+2500 n\) dollars per year at the end of the \(n\) th year. Write a sequence showing her salary at the end of each of the first 5 yr. If she continues in this way, what will her salary be at the end of the tenth year?

Write each series as a sum of terms and then find the sum. $$ \sum_{i=1}^{6}(i+9) $$

Evaluate the sum of the terms of each geometric sequence. In Exercises 39-44, give answers to the nearest thousandth. See Examples 5 and 6. $$ \sum_{i=1}^{6}(-2)\left(-\frac{1}{2}\right)^{i} $$

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