Calculate the Average: Finding Mean of 1, 2, and 33

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

Average and mean are the same thing! Both terms refer to adding all values and dividing by the count. You might also hear 'arithmetic mean' - that's the same concept too.

Q: Do I always divide by 3 when finding averages?

No! You divide by however many numbers you have. In this problem we have 3 numbers (1, 2, 33), so we divide by 3. If you had 5 numbers, you'd divide by 5.

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

Your average should be between the smallest and largest values. Here, 12 is between 1 and 33, so it makes sense. If your answer was 50 or -5, you'd know something went wrong!

Q: What if the sum doesn't divide evenly?

That's totally normal! Many averages are decimal numbers. For example, the average of 1, 2, and 4 would be $ \frac{7}{3} = 2.33... $

Arithmetic Mean with Mixed Numbers

Calculate the average

of $1$ , $2$ , and $33$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the average

00:03 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)

00:27 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 $1$ , $2$ , and $33$ .

Step-by-step solution

To solve this problem, we will calculate the average of the numbers 1, 2, and 33 using the arithmetic mean formula.

The steps to find the average are as follows:

Step 1: Calculate the sum of the numbers: $1 + 2 + 33 = 36$ .
Step 2: Count the number of terms: There are 3 terms.
Step 3: Find the average by dividing the sum by the number of terms: $\frac{36}{3} = 12$ .

Therefore, the average of the numbers 1, 2, and 33 is $12$ .

This corresponds to choice 4 in the provided options.

Thus, the solution to the problem is $12$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum of all values divided by count
Technique: Add 1 + 2 + 33 = 36, then divide by 3
Check: Verify that $\frac{36}{3} = 12$ makes sense ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by the number of values
Don't just add the numbers 1 + 2 + 33 = 36 and call that the average! This gives you the sum, not the average. Always divide the sum by how many numbers you have: 36 ÷ 3 = 12.

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 12 when most of my numbers are small?

The large number 33 pulls the average up significantly! Even though you have 1 and 2, the 33 has a big impact. This shows how outliers (unusually large or small values) affect the mean.

What's the difference between average and mean?

Average and mean are the same thing! Both terms refer to adding all values and dividing by the count. You might also hear 'arithmetic mean' - that's the same concept too.

Do I always divide by 3 when finding averages?

No! You divide by however many numbers you have. In this problem we have 3 numbers (1, 2, 33), so we divide by 3. If you had 5 numbers, you'd divide by 5.

How can I check if my average makes sense?

Your average should be between the smallest and largest values. Here, 12 is between 1 and 33, so it makes sense. If your answer was 50 or -5, you'd know something went wrong!

What if the sum doesn't divide evenly?

That's totally normal! Many averages are decimal numbers. For example, the average of 1, 2, and 4 would be $\frac{7}{3} = 2.33...$

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