Calculate Average: Finding Mean of 7 Numbers with Sum 28

Q: Why do I divide instead of multiply?

Think of it this way: if you have 28 items shared equally among 7 people, each person gets 28 ÷ 7 = 4 items. The average is how much each "position" would get if everything was distributed evenly.

Q: What if the division doesn't come out evenly?

That's completely normal! Averages can be decimals or fractions. For example, if the sum was 29, the average would be 29 ÷ 7 = 4.14 (approximately).

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

Multiply your average by the number of values: average × count = original sum. Here: 4 × 7 = 28 ✓. If you don't get back the original sum, recalculate!

Q: Does the order of the seven numbers matter?

No! The average only depends on the sum and count of numbers. Whether the numbers are 1,2,3,4,5,6,7 or 0,0,0,0,0,0,28, the average is still 4.

Q: What's the difference between mean and average?

They're the same thing! "Mean" is the mathematical term, while "average" is the everyday word. Both use the formula: $ \frac{\text{sum}}{\text{count}} $

Average Formula with Division Operations

What is the average of seven numbers with a sum of 28?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the average of these numbers.

00:07 To do this, we'll add them up and divide by how many numbers there are.

00:12 Since we already have the total sum, let's substitute it in and divide by the total number of numbers.

00:19 And that's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the average of seven numbers with a sum of 28?

Step-by-step solution

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

Step 1: Identify the given data
Step 2: Use the average formula
Step 3: Perform the division to find the average

Now, let's work through each step:

Step 1: The total sum of the numbers is given as $28$ , and there are $7$ numbers.

Step 2: We'll use the formula for calculating the average:

$\text{Average} = \frac{\text{Sum of values}}{\text{Number of values}}$

Step 3: Plugging in the values, we have:

$\text{Average} = \frac{28}{7}$

$\text{Average} = 4$

Therefore, the solution to the problem is that the average of these seven numbers is $\mathbf{4}$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum of values divided by number of values
Technique: Set up $\frac{28}{7} = 4$ for direct calculation
Check: Verify 4 × 7 = 28 matches original sum ✓

Common Mistakes

Avoid these frequent errors

Confusing sum with average
Don't give 28 as the answer = mixing up given information with what you're solving for! The sum (28) is what you start with, not the final answer. Always divide the sum by the count to find the average.

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 do I divide instead of multiply?

Think of it this way: if you have 28 items shared equally among 7 people, each person gets 28 ÷ 7 = 4 items. The average is how much each "position" would get if everything was distributed evenly.

What if the division doesn't come out evenly?

That's completely normal! Averages can be decimals or fractions. For example, if the sum was 29, the average would be 29 ÷ 7 = 4.14 (approximately).

How can I check if my average is reasonable?

Multiply your average by the number of values: average × count = original sum. Here: 4 × 7 = 28 ✓. If you don't get back the original sum, recalculate!

Does the order of the seven numbers matter?

No! The average only depends on the sum and count of numbers. Whether the numbers are 1,2,3,4,5,6,7 or 0,0,0,0,0,0,28, the average is still 4.

What's the difference between mean and average?

They're the same thing! "Mean" is the mathematical term, while "average" is the everyday word. Both use the formula: $\frac{\text{sum}}{\text{count}}$

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