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?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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 \( 10 \) and \( 12 \).

FAQ

Everything you need to know about this question

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

+

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?

+

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?

+

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?

+

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?

+

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!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Data Exploration questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations