Calculate the Average: Finding the Mean of 30, 1, 2, and 3

Q: Why is the average 9 when most numbers are small?

The average considers all values equally! Even though 1, 2, and 3 are small, the large value 30 pulls the average up significantly. That's how averages work - they balance out all the numbers.

Q: Do I always add first, then divide?

Yes, always! The average formula requires the total sum divided by the count. You can't find the average any other way - addition must come before division.

Q: Can the average be bigger than some of the original numbers?

Absolutely! In this problem, the average (9) is bigger than three of the original numbers (1, 2, 3) but smaller than the largest (30). Averages can fall anywhere within or even outside the range of your data.

Q: How do I check if my average is reasonable?

Look at your numbers! The average should be somewhere between the smallest and largest values. Here, 9 falls between 1 and 30, so it makes sense. If you got 40 or 0, you'd know something went wrong.

Average Calculation with Mixed Value Sets

Calculate the average

of $30,1,2,$ and $3$ .

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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

00:08 Let's sum up the numbers

00:17 and divide by the number of occurrences (4)

00:31 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 $30,1,2,$ and $3$ .

Step-by-step solution

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

Step 1: Add up all the numbers given.
Step 2: Count the total number of numbers.
Step 3: Divide the sum by the total number to find the average.

Let's work through each step:

Step 1: Compute the sum of the numbers.

$30 + 1 + 2 + 3 = 36$

Step 2: Count the total number of numbers. Here, we have 4 numbers.

Step 3: Use the formula for the average:

$\text{Average} = \frac{\text{Sum of all numbers}}{\text{Total number of numbers}}$

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

Based on the calculation, the average of the numbers 30, 1, 2, and 3 is $\mathbf{9}$ .

Thus, the correct answer is $\mathbf{9}$ , which corresponds to choice id "1" in the answer choices.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum of all numbers divided by count
Technique: Add all values first: 30 + 1 + 2 + 3 = 36
Check: Verify by multiplying average by count: 9 × 4 = 36 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count all numbers when dividing
Don't just divide the sum by 3 because you see three small numbers = wrong average of 12! The large number 30 is still one value that must be counted. Always count every single number in your set, regardless of size.

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 9 when most numbers are small?

The average considers all values equally! Even though 1, 2, and 3 are small, the large value 30 pulls the average up significantly. That's how averages work - they balance out all the numbers.

Do I always add first, then divide?

Yes, always! The average formula requires the total sum divided by the count. You can't find the average any other way - addition must come before division.

What if I accidentally skip counting one number?

You'll get the wrong answer! If you divided 36 by 3 instead of 4, you'd get 12 instead of 9. Always double-check that you've counted every single number in your list.

Can the average be bigger than some of the original numbers?

Absolutely! In this problem, the average (9) is bigger than three of the original numbers (1, 2, 3) but smaller than the largest (30). Averages can fall anywhere within or even outside the range of your data.

How do I check if my average is reasonable?

Look at your numbers! The average should be somewhere between the smallest and largest values. Here, 9 falls between 1 and 30, so it makes sense. If you got 40 or 0, you'd know something went wrong.

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