Calculate Average: Finding Mean of Three Numbers with Sum 10

Average Calculation with Fixed Sum

What is the average of three numbers that have a sum of 10?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the average of the numbers
00:03 To calculate the average, sum and divide by the number of occurrences
00:06 Insert the given sum, and divide by the quantity of numbers
00:09 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the average of three numbers that have a sum of 10?

2

Step-by-step solution

To solve this problem, we need to find the average of three numbers that sum up to 10.

We will follow these steps:

  • Step 1: Identify the sum of the numbers, which is given as 10.
  • Step 2: Identify the number of terms, which in this case is 3.
  • Step 3: Apply the average formula Average=Sum of numbersn \text{Average} = \frac{\text{Sum of numbers}}{n} .

Now, let's perform the calculations:
Step 1: The sum of the three numbers is 10 10 .
Step 2: There are 3 3 numbers to consider.
Step 3: Calculate the average:Average=103=3.3333 \text{Average} = \frac{10}{3} = 3.3333\ldots .

We can express 3.3333 3.3333\ldots as a mixed number: 313 3\frac{1}{3} .

Therefore, the average of three numbers that sum to 10 is 313 3\frac{1}{3} .

3

Final Answer

313 3\frac{1}{3}

Key Points to Remember

Essential concepts to master this topic
  • Formula: Average equals sum divided by number of values
  • Technique: 103=313 \frac{10}{3} = 3\frac{1}{3} by converting improper to mixed number
  • Check: Multiply answer by count: 313×3=10 3\frac{1}{3} \times 3 = 10

Common Mistakes

Avoid these frequent errors
  • Dividing by the sum instead of number of values
    Don't divide 3 by 10 = 0.3! This reverses the formula and gives a decimal less than 1. Always divide the sum by the count of numbers using Average = Sum ÷ Count.

Practice Quiz

Test your knowledge with interactive questions

Calculate the average of \( 11 \) and \( 7 \).

FAQ

Everything you need to know about this question

Why is the average a mixed number instead of a whole number?

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When the sum doesn't divide evenly by the count, you get a mixed number or decimal. Since 10÷3 10 ÷ 3 doesn't divide evenly, we get 313 3\frac{1}{3} .

How do I convert the improper fraction to a mixed number?

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Divide the numerator by denominator: 103 \frac{10}{3} means 10 ÷ 3 = 3 remainder 1, so the answer is 313 3\frac{1}{3} .

Can I just leave my answer as a decimal?

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Yes! 313=3.333... 3\frac{1}{3} = 3.333... But since the answer choices are mixed numbers, it's better to convert to mixed number form for matching.

What if I don't know what the three numbers are?

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That's okay! You don't need to know the individual numbers. The average formula only requires the sum and count, which you have.

How can I check if my answer is correct?

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Multiply your average by the number of values: 313×3=103×3=10 3\frac{1}{3} \times 3 = \frac{10}{3} \times 3 = 10 . If you get the original sum, you're right!

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