Calculate the Average: Finding Mean of 11, 13, 4, and 9

Q: Why is the answer a mixed number instead of a decimal?

Both forms are correct! $ 9\frac{1}{4} $ and 9.25 represent the same value. Mixed numbers are often preferred because they show the exact fractional part clearly.

Q: How do I convert 37/4 to a mixed number?

Divide 37 by 4: 37 ÷ 4 = 9 remainder 1. The quotient (9) becomes the whole number, and the remainder (1) goes over the divisor (4), giving you $ 9\frac{1}{4} $.

Q: What if I added the numbers wrong?

Double-check your addition step by step: 11 + 13 = 24, then 24 + 4 = 28, finally 28 + 9 = 37. You can also add in a different order to verify.

Q: Can the average be larger than all the original numbers?

No! The average must always fall between the smallest and largest values. Here, our average $ 9\frac{1}{4} $ is between 4 and 13, which makes sense.

Q: Do I always divide by 4 when finding an average?

No! You divide by however many numbers you have. If you had 5 numbers, divide by 5. If you had 10 numbers, divide by 10. Always count your values first.

Average Calculation with Mixed Numbers

Calculate the average

of $11,13,4,$ and $9$ .

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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

00:13 And divide by the number of occurrences (4)

00:31 Let's break down 37 into 36 plus 1

00:41 Let's break it down into whole number and remainder

00:45 Convert from whole fraction to whole number

00:51 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 $11,13,4,$ and $9$ .

Step-by-step solution

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

Step 1: Calculate the sum of the numbers.
Step 2: Divide the sum by the number of values to find the average.

Now, let's work through each step:
Step 1: The numbers given are 11, 13, 4, and 9. We calculate the sum as follows:
$11 + 13 + 4 + 9 = 37$ .
Step 2: To find the average, divide the sum by 4 (the number of values):
$\frac{37}{4} = 9.25$ or $9\frac{1}{4}$ when expressed as a mixed number.

Therefore, the average of 11, 13, 4, and 9 is $9\frac{1}{4}$ .

Final Answer

$9\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum divided by count of numbers
Technique: Sum all values first: 11 + 13 + 4 + 9 = 37
Check: Multiply answer by count: $9\frac{1}{4} \times 4 = 37$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count all the numbers when dividing
Don't divide by 3 when you have 4 numbers = wrong average! Students often miscount the values, especially when numbers are written separately. Always count each number carefully: 11, 13, 4, and 9 means divide by 4.

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 is the answer a mixed number instead of a decimal?

Both forms are correct! $9\frac{1}{4}$ and 9.25 represent the same value. Mixed numbers are often preferred because they show the exact fractional part clearly.

How do I convert 37/4 to a mixed number?

Divide 37 by 4: 37 ÷ 4 = 9 remainder 1. The quotient (9) becomes the whole number, and the remainder (1) goes over the divisor (4), giving you $9\frac{1}{4}$ .

What if I added the numbers wrong?

Double-check your addition step by step: 11 + 13 = 24, then 24 + 4 = 28, finally 28 + 9 = 37. You can also add in a different order to verify.

Can the average be larger than all the original numbers?

No! The average must always fall between the smallest and largest values. Here, our average $9\frac{1}{4}$ is between 4 and 13, which makes sense.

Do I always divide by 4 when finding an average?

No! You divide by however many numbers you have. If you had 5 numbers, divide by 5. If you had 10 numbers, divide by 10. Always count your values first.

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