Calculate Average: Finding Mean When Sum Equals 15

Q: Why do I need to convert the decimal to a mixed number?

Converting 3.75 to 3¾ makes the answer clearer and matches the format of the answer choices. Both forms are correct, but mixed numbers are often preferred in math problems.

Q: What if the sum doesn't divide evenly?

That's normal! Averages are often fractions or decimals. Just divide the sum by the count of numbers and express your answer in the form requested.

Q: How can I check if my average is reasonable?

Your average should be between the smallest and largest possible values. Since we have 4 numbers summing to 15, the average should be close to what each number might be.

Q: Does it matter what the actual four numbers are?

No! As long as four numbers add up to 15, their average will always be $ \frac{15}{4} = 3\frac{3}{4} $, regardless of the individual values.

Q: Can I use this same method for any number of values?

Yes! The formula Average = Sum ÷ Count works for any amount of numbers. Just make sure you count correctly and divide by the right number.

Average Calculation with Mixed Number Results

What is the average of four numbers that have a sum of 15?

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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, we sum and divide by the number of occurrences

00:06 We already have the sum, so we'll substitute and divide by the quantity of numbers

00:10 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the average of four numbers that have a sum of 15?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate formula to find the average
Step 3: Perform the calculation to find the result

Now, let's go through each step:

Step 1: The problem tells us the sum of four numbers is 15.

Step 2: We will use the formula for average: $\text{Average} = \frac{\text{Sum of numbers}}{n}$ , where $n$ is the number of numbers.

Step 3: Substituting into the formula, we have:

$\text{Average} = \frac{15}{4}$

Calculating this gives:

$\frac{15}{4} = 3.75$

We can express $3.75$ as a mixed number: $3\frac{3}{4}$ .

Therefore, the average of the four numbers is $3\frac{3}{4}$ .

Final Answer

$3\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum divided by number of values
Technique: Convert $\frac{15}{4} = 3.75 = 3\frac{3}{4}$
Check: Multiply average by count: $3\frac{3}{4} \times 4 = 15$ ✓

Common Mistakes

Avoid these frequent errors

Dividing sum by wrong number of values
Don't divide 15 by 3 instead of 4 = 5 instead of 3¾! Students often miscount or use the sum instead of the count. Always carefully identify how many numbers you have before dividing.

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 do I need to convert the decimal to a mixed number?

Converting 3.75 to 3¾ makes the answer clearer and matches the format of the answer choices. Both forms are correct, but mixed numbers are often preferred in math problems.

What if the sum doesn't divide evenly?

That's normal! Averages are often fractions or decimals. Just divide the sum by the count of numbers and express your answer in the form requested.

How can I check if my average is reasonable?

Your average should be between the smallest and largest possible values. Since we have 4 numbers summing to 15, the average should be close to what each number might be.

Does it matter what the actual four numbers are?

No! As long as four numbers add up to 15, their average will always be $\frac{15}{4} = 3\frac{3}{4}$ , regardless of the individual values.

Can I use this same method for any number of values?

Yes! The formula Average = Sum ÷ Count works for any amount of numbers. Just make sure you count correctly and divide by the right number.

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