Find Number Groups with Mean Value 8: Average Selection Challenge

Q: How can different number groups have the same average?

The average depends on the total sum and count, not the individual numbers! For example, (10,8,12,2) and (24,0,0) both average to 8 because $ \frac{32}{4} = \frac{24}{3} = 8 $.

Q: Do I need to check all choices even if I find one that works?

Yes, always check every option! The question might have multiple correct answers, and you could miss the "All answers are correct" choice if you stop too early.

Q: What's the fastest way to calculate these averages?

Add all numbers in the groupCount how many numbers there areDivide the sum by the countCompare your result to 8

Average Calculation with Multiple Choice Verification

Choose the group of numbers of which 8 is the average.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's start by finding the group with an average of 8.

00:08 To calculate the average, add up all the numbers, then divide by how many numbers there are.

00:14 We'll use this simple formula to find the mean. Ready? Let's do it together.

00:29 Great! That's the average. Now, let's check out the next group.

00:34 Using the same average formula, let's find the mean for this one too.

00:42 Awesome! We got the average. Time to move on to the next group.

00:47 If every number in the group is the same, the average is simply that number. Easy, right?

00:52 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

Choose the group of numbers of which 8 is the average.

Step-by-step solution

To solve this problem, we'll follow these steps to verify if each group of numbers has an average of 8:

Calculate the average for each group of numbers provided in the answer choices.

Let's calculate:

Choice 1: $10, 8, 12, 2$
Sum = $10 + 8 + 12 + 2 = 32$
Count = 4
Average = $\frac{32}{4} = 8$
Choice 2: $24, 0, 0$
Sum = $24 + 0 + 0 = 24$
Count = 3
Average = $\frac{24}{3} = 8$
Choice 3: $8, 8, 8$
Sum = $8 + 8 + 8 = 24$
Count = 3
Average = $\frac{24}{3} = 8$

Therefore, all choices result in an average of 8.

This verifies that All answers are correct.

Final Answer

All answers are correct.

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum of values divided by count of values
Technique: Calculate sum first: 10 + 8 + 12 + 2 = 32, then divide by 4
Check: Verify each group separately to confirm all have average 8 ✓

Common Mistakes

Avoid these frequent errors

Assuming only one answer can be correct
Don't automatically eliminate other choices after finding one correct answer = missing the "All answers correct" option! Multiple number groups can have the same average. Always check every single choice before selecting your final answer.

Practice Quiz

Test your knowledge with interactive questions

If the balls below are divided so that each column in the table contains an equal number, then how many balls will there be in each column?

FAQ

Everything you need to know about this question

How can different number groups have the same average?

The average depends on the total sum and count, not the individual numbers! For example, (10,8,12,2) and (24,0,0) both average to 8 because $\frac{32}{4} = \frac{24}{3} = 8$ .

What if I get a decimal when calculating the average?

That's normal! Averages don't have to be whole numbers. Just make sure to divide accurately and round only if the problem asks for it.

Do I need to check all choices even if I find one that works?

Yes, always check every option! The question might have multiple correct answers, and you could miss the "All answers are correct" choice if you stop too early.

Can the average be one of the numbers in the group?

Absolutely! In the group (8,8,8), the average is 8, which is also each individual value. This happens when all numbers in the group are the same.

What's the fastest way to calculate these averages?

Add all numbers in the group
Count how many numbers there are
Divide the sum by the count
Compare your result to 8

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