Calculate the Average: Finding the Mean of Four 10s

Q: Why is the average of identical numbers always that same number?

When all values are the same, they balance perfectly! Think of it like having 4 groups with exactly 10 items each - the average per group is still 10.

Q: Do I still need to do the full calculation when numbers are identical?

It's good practice to show the work: $ \frac{10+10+10+10}{4} = \frac{40}{4} = 10 $. This proves you understand the process and helps avoid careless errors.

Q: How do I remember the average formula?

Think: "Share equally". If you have 40 candies to share equally among 4 friends, each gets $ \frac{40}{4} = 10 $ candies!

Q: Can the average ever be bigger than all the original numbers?

No! The average is always between the smallest and largest values in your set. It represents the "middle ground" of your data.

Finding Averages with Identical Values

Calculate the average of

$10$ , $10$ , $10$ , and $10$ .

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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

00:07 Let's sum up the numbers

00:12 and divide by the number of occurrences (4)

00:32 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

$10$ , $10$ , $10$ , and $10$ .

Step-by-step solution

To solve the problem of finding the average of the numbers $10, 10, 10, 10$ , follow these steps:

Step 1: Calculate the sum of the numbers. Here, since the numbers are identical, the sum is $10 + 10 + 10 + 10 = 40$ .
Step 2: Divide the total sum by the number of numbers, which is 4. Therefore, the average is $\frac{40}{4} = 10$ .

Thus, the average of the numbers is $10$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Average equals sum of values divided by count
Technique: When all values are identical, the average equals that value
Check: Substitute back: $\frac{10+10+10+10}{4} = \frac{40}{4} = 10$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by the number of values
Don't just add the numbers and stop at 40! This gives the sum, not the average. The sum tells you the total, but not the typical value. Always divide the sum by how many numbers you counted.

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 is the average of identical numbers always that same number?

When all values are the same, they balance perfectly! Think of it like having 4 groups with exactly 10 items each - the average per group is still 10.

Do I still need to do the full calculation when numbers are identical?

It's good practice to show the work: $\frac{10+10+10+10}{4} = \frac{40}{4} = 10$ . This proves you understand the process and helps avoid careless errors.

What if I have 100 tens instead of just 4?

The average is still 10! With identical values, the average never changes regardless of how many numbers you have.

How do I remember the average formula?

Think: "Share equally". If you have 40 candies to share equally among 4 friends, each gets $\frac{40}{4} = 10$ candies!

Can the average ever be bigger than all the original numbers?

No! The average is always between the smallest and largest values in your set. It represents the "middle ground" of your data.

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