Calculate the Average of Numbers: 10, 3, 2, and 4

Q: Should I leave my answer as 19/4 or convert to mixed number?

Both forms are correct! $ \frac{19}{4} $ and $ 4\frac{3}{4} $ mean the same thing. Mixed numbers are often easier to understand because they show the whole number part clearly.

Q: How do I convert 19/4 to a mixed number?

Divide 19 by 4: 19 ÷ 4 = 4 remainder 3. The quotient (4) becomes the whole number, and the remainder (3) goes over the original denominator (4): $ 4\frac{3}{4} $

Q: Can I check my answer by working backwards?

Yes! Multiply your average by the count: $ 4\frac{3}{4} \times 4 = \frac{19}{4} \times 4 = 19 $. This should equal your original sum!

Q: What if I need the answer as a decimal?

Just divide: $ \frac{19}{4} = 19 ÷ 4 = 4.75 $. All three forms are equivalent: $ \frac{19}{4} = 4\frac{3}{4} = 4.75 $

Mean Calculation with Mixed Numbers

Calculate the average

of $10,3,2,$ and $4$ .

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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

00:15 and divide by the number of occurrences (4)

00:30 Let's break down 19 into 19 plus 3

00:37 Let's break it down into whole number and remainder

00:44 Convert from proper fraction to whole number

00:48 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 $10,3,2,$ and $4$ .

Step-by-step solution

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

Step 1: Calculate the sum of the numbers.
Step 2: Count the number of numbers given.
Step 3: Divide the sum by the count to find the average.

Now, let's work through each step:

Step 1: Add the numbers $10 + 3 + 2 + 4$ .

$10 + 3 + 2 + 4 = 19$ .

Step 2: Count the number of numbers, which is 4.

Step 3: Divide the total sum by the number of numbers: $\frac{19}{4}$ .

$\frac{19}{4}$ can be written as a mixed number, which is $4\frac{3}{4}$ .

Therefore, the average of 10, 3, 2, and 4 is $4\frac{3}{4}$ .

Final Answer

$4\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum divided by count of numbers
Technique: Add 10 + 3 + 2 + 4 = 19, then divide by 4
Check: Convert $\frac{19}{4} = 4\frac{3}{4}$ back to decimal: 4.75 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count all numbers when dividing
Don't count wrong like dividing 19 by 3 instead of 4 = getting 6.33! This happens when you miscount the given numbers. Always count each number carefully: 10, 3, 2, 4 equals exactly 4 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 get a fraction instead of a whole number?

Averages don't have to be whole numbers! When the sum doesn't divide evenly by the count, you get a fraction or decimal. That's completely normal and correct.

Should I leave my answer as 19/4 or convert to mixed number?

Both forms are correct! $\frac{19}{4}$ and $4\frac{3}{4}$ mean the same thing. Mixed numbers are often easier to understand because they show the whole number part clearly.

How do I convert 19/4 to a mixed number?

Divide 19 by 4: 19 ÷ 4 = 4 remainder 3. The quotient (4) becomes the whole number, and the remainder (3) goes over the original denominator (4): $4\frac{3}{4}$

Can I check my answer by working backwards?

Yes! Multiply your average by the count: $4\frac{3}{4} \times 4 = \frac{19}{4} \times 4 = 19$ . This should equal your original sum!

What if I need the answer as a decimal?

Just divide: $\frac{19}{4} = 19 ÷ 4 = 4.75$ . All three forms are equivalent: $\frac{19}{4} = 4\frac{3}{4} = 4.75$

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