Calculate the Average of the Number Sequence: 7, 9, 12, 8

Q: Why do I need to count the numbers first?

The average formula is sum ÷ count, so you need both parts! If you miscount, you'll get the wrong average even if your addition is perfect.

Q: What if the numbers don't add up to a number divisible by the count?

That's totally normal! Many averages are decimals or fractions. For example, the average of 7, 8, 9 is $ \frac{24}{3} = 8 $, but the average of 7, 8, 10 is $ \frac{25}{3} = 8.33... $

Q: How can I check if my average makes sense?

Your average should be between the smallest and largest numbers. Here, 9 is between 7 and 12, so it makes sense! If your average is outside this range, recheck your work.

Q: Do I need to arrange the numbers in order first?

No! The order doesn't matter for finding the average. Whether you write 7, 9, 12, 8 or 8, 7, 12, 9, the sum and count stay the same.

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

They're the same thing! Average, mean, and arithmetic mean all refer to the sum divided by the count. Don't get confused by different names - the calculation is identical.

Average Calculation with Mixed Numbers

Calculate the average

of $7,9,12,$ and $8$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the average

00:04 To calculate the average, we need to divide the sum by the number of occurrences

00:09 Let's sum up the numbers

00:16 and divide by the number of occurrences (4)

00:34 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

Calculate the average

of $7,9,12,$ and $8$ .

Step-by-step solution

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

Step 1: Add the numbers given.
Step 2: Divide the sum by the number of terms.
Step 3: Verify the result against the given answer choices.

Let's work through each step:

Step 1: The problem provides the numbers $7, 9, 12,$ and $8$ .
Calculate the sum: $7 + 9 + 12 + 8 = 36$ .

Step 2: There are four numbers. To find the average, divide the sum by the count of numbers:
$\text{Average} = \frac{36}{4} = 9$ .

Therefore, the average of the numbers $7, 9, 12, 8$ is $9$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Add all numbers, then divide by count of terms
Technique: Sum: 7 + 9 + 12 + 8 = 36, then divide by 4
Check: Average × count should equal sum: 9 × 4 = 36 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count all numbers correctly
Don't just divide by 3 when there are 4 numbers = $\frac{36}{3} = 12$ which is wrong! Students often miscount when numbers are written in different ways. Always count each individual number carefully: 7, 9, 12, and 8 makes 4 numbers total.

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 count the numbers first?

The average formula is sum ÷ count, so you need both parts! If you miscount, you'll get the wrong average even if your addition is perfect.

What if the numbers don't add up to a number divisible by the count?

That's totally normal! Many averages are decimals or fractions. For example, the average of 7, 8, 9 is $\frac{24}{3} = 8$ , but the average of 7, 8, 10 is $\frac{25}{3} = 8.33...$

How can I check if my average makes sense?

Your average should be between the smallest and largest numbers. Here, 9 is between 7 and 12, so it makes sense! If your average is outside this range, recheck your work.

Do I need to arrange the numbers in order first?

No! The order doesn't matter for finding the average. Whether you write 7, 9, 12, 8 or 8, 7, 12, 9, the sum and count stay the same.

What's the difference between average, mean, and arithmetic mean?

They're the same thing! Average, mean, and arithmetic mean all refer to the sum divided by the count. Don't get confused by different names - the calculation is identical.

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