Calculate the Average: Finding Mean of 10, 5, and 15

Q: Should my answer be between the smallest and largest numbers?

Yes! The average should always fall between your smallest (5) and largest (15) values. If your answer is outside this range, double-check your work.

Q: Is there a faster way to check if my answer makes sense?

Yes! Ask yourself: "Is my answer reasonable?" Since 10 is one of the original numbers and the others (5, 15) balance around it, 10 makes perfect sense as the average.

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

They're all the same thing! Mean, average, and arithmetic mean all refer to adding up all values and dividing by the count. Don't get confused by the different names.

Mean Calculation with Three Numbers

Calculate the average

of $10$ , $5$ , and $15$ .

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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

00:11 And divide by the number of occurrences (3)

00:30 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 $10$ , $5$ , and $15$ .

Step-by-step solution

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

Step 1: Identify the given numbers: 10, 5, and 15.
Step 2: Apply the formula for the average.
Step 3: Perform the calculation to find the average.

Now, let's work through each step:

Step 1: We have three numbers to consider: $10$ , $5$ , and $15$ .

Step 2: To find the average, we use the formula:

$\text{Average} = \frac{\text{Sum of the numbers}}{\text{Number of numbers}}$

Step 3: Calculate the sum of the numbers:

$10 + 5 + 15 = 30$

Step 4: Divide the sum by the number of numbers:

The number of numbers is 3, so:

$\text{Average} = \frac{30}{3} = 10$

Therefore, the average of 10, 5, and 15 is $10$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum of numbers divided by count
Technique: Add all values first: 10 + 5 + 15 = 30
Check: Verify 30 ÷ 3 = 10 lies between smallest and largest values ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by the number of values
Don't just add the numbers and stop at 30! This gives you the sum, not the average. The average requires dividing by how many numbers you have. Always divide the sum by the count of numbers.

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 by 3 and not by something else?

You divide by 3 because that's how many numbers you're averaging! Count them: 10, 5, and 15 makes three numbers. Always count your data points carefully.

Should my answer be between the smallest and largest numbers?

Yes! The average should always fall between your smallest (5) and largest (15) values. If your answer is outside this range, double-check your work.

What if I get a decimal answer instead of a whole number?

That's completely normal! Not all averages are whole numbers. For example, the average of 1, 2, and 5 is $\frac{8}{3} = 2.67$ .

Is there a faster way to check if my answer makes sense?

Yes! Ask yourself: "Is my answer reasonable?" Since 10 is one of the original numbers and the others (5, 15) balance around it, 10 makes perfect sense as the average.

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

They're all the same thing! Mean, average, and arithmetic mean all refer to adding up all values and dividing by the count. Don't get confused by the different names.

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