Calculate Average: Verify if 10 Equals Mean of (8,11,10,7)

Q: Why do I add all the numbers first instead of comparing individually?

You need the average (mean) of the group, not individual comparisons! The average represents the single value that best describes the whole group of numbers.

Q: How do I remember which comparison symbol to use?

After calculating the mean, ask yourself: "Is 10 bigger or smaller than my calculated average?" If 10 is bigger, use >. If smaller, use

Q: What if I get a decimal or fraction for the average?

That's completely normal! Averages don't have to be whole numbers. For example, if the sum was 37, the average would be $ \frac{37}{4} = 9.25 $, and you'd still compare this to 10.

Q: Can the average ever equal one of the original numbers?

Yes! Sometimes the calculated mean matches one of the values in your list. In this problem, one number was 10, but the average was 9, so they're different.

Q: What does the notation with the question mark mean?

The $ \stackrel{?}{=} $ notation means "fill in the correct comparison symbol". You need to determine whether to use based on your calculation.

Mean Calculation with Comparison Operations

Calculate the average of each group and choose the appropriate sign (?):

$10\stackrel{?}{=}8,11,10,7$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 To find the average of each group, let's calculate carefully.

00:14 We do this by dividing the total sum by the number of items.

00:22 That's how we find the average. Now, let's repeat for the second group using the same steps.

01:02 Finally, let's compare the results and choose the correct sign.

01:07 And that's how we solve this problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the average of each group and choose the appropriate sign (?):

$10\stackrel{?}{=}8,11,10,7$

Step-by-step solution

Let's solve the problem step by step:

Step 1: Calculate the sum of the numbers. The numbers given are $8, 11, 10,$ and $7$ .

Sum = $8 + 11 + 10 + 7 = 36$ .

Step 2: Find the average using the formula $\frac{\text{Sum}}{\text{Number of elements}}$ .

The number of elements is $4$ .

Average = $\frac{36}{4} = 9$ .

Step 3: Compare the average with $10$ .

Since $9$ is less than $10$ , we have $9 < 10$ .

Therefore, the correct sign to fill in the blank is $\gt$ because we are comparing $10$ (the number on the left) with $9$ (the average) and since $10$ is greater, $10\gt8,11,10,7$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum divided by number of values
Technique: Sum = 8+11+10+7 = 36, then divide by 4 values
Check: Compare calculated mean 9 with given value 10: since 9 < 10, then 10 > 9 ✓

Common Mistakes

Avoid these frequent errors

Confusing comparison direction when writing inequality
Don't write 10 < 9 when the mean is 9 and you're comparing to 10 = backwards inequality! This reverses the relationship and gives the wrong comparison symbol. Always think: 10 is greater than 9, so write 10 > 9.

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

Why do I add all the numbers first instead of comparing individually?

You need the average (mean) of the group, not individual comparisons! The average represents the single value that best describes the whole group of numbers.

How do I remember which comparison symbol to use?

After calculating the mean, ask yourself: "Is 10 bigger or smaller than my calculated average?" If 10 is bigger, use >. If smaller, use <. If equal, use =.

What if I get a decimal or fraction for the average?

That's completely normal! Averages don't have to be whole numbers. For example, if the sum was 37, the average would be $\frac{37}{4} = 9.25$ , and you'd still compare this to 10.

Can the average ever equal one of the original numbers?

Yes! Sometimes the calculated mean matches one of the values in your list. In this problem, one number was 10, but the average was 9, so they're different.

What does the notation with the question mark mean?

The $\stackrel{?}{=}$ notation means "fill in the correct comparison symbol". You need to determine whether to use <, =, or > based on your calculation.

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