Calculate the Average: Finding Mean of 1, 11, 3, and 1

Q: Do I count repeated numbers separately?

Yes, absolutely! Each number in the list counts as one value, even if it's repeated. In this problem, we have four values: 1, 11, 3, and 1.

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

They're the same thing! Mean and average both refer to adding all values and dividing by the count. The terms can be used interchangeably.

Q: Why isn't the answer 11 since it's the biggest number?

The average considers all values equally, not just the largest. The small numbers (1, 3, 1) balance out the large number (11) to give us 4.

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

Your average should be between the smallest and largest values. Since our numbers range from 1 to 11, an average of 4 makes perfect sense!

Q: What if I accidentally add the numbers wrong?

Double-check your addition: $ 1 + 11 = 12 $, then $ 12 + 3 = 15 $, then $ 15 + 1 = 16 $. Always verify your sum before dividing!

Finding Average with Multiple Repeated Values

Calculate the average of:

$1,11,3,$ and $1$ .

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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 add 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:

$1,11,3,$ and $1$ .

Step-by-step solution

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

Step 1: Sum the numbers
Step 2: Divide the sum by the number of numbers

Now, let's work through each step:
Step 1: Calculate the sum of the numbers:
$1 + 11 + 3 + 1 = 16$

Step 2: Divide the sum by the total number of numbers. There are 4 numbers, so we divide 16 by 4:
$\frac{16}{4} = 4$

Therefore, the average of the numbers is $\textbf{4}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum of all values divided by count
Technique: Add all numbers: 1 + 11 + 3 + 1 = 16
Check: Verify by counting values correctly: 4 numbers total ✓

Common Mistakes

Avoid these frequent errors

Miscounting the total number of values
Don't count 1, 11, 3, 1 as only 3 different numbers = $\frac{16}{3} = 5.33$ wrong answer! Repeated values still count as separate data points. Always count each individual value in the list, even if some numbers appear multiple times.

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

Do I count repeated numbers separately?

Yes, absolutely! Each number in the list counts as one value, even if it's repeated. In this problem, we have four values: 1, 11, 3, and 1.

What's the difference between mean and average?

They're the same thing! Mean and average both refer to adding all values and dividing by the count. The terms can be used interchangeably.

Why isn't the answer 11 since it's the biggest number?

The average considers all values equally, not just the largest. The small numbers (1, 3, 1) balance out the large number (11) to give us 4.

How can I check if my average makes sense?

Your average should be between the smallest and largest values. Since our numbers range from 1 to 11, an average of 4 makes perfect sense!

What if I accidentally add the numbers wrong?

Double-check your addition: $1 + 11 = 12$ , then $12 + 3 = 15$ , then $15 + 1 = 16$ . Always verify your sum before dividing!

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