Calculate the Average of the Sequence: 21, 0, 0, 0

Q: Do I really need to count the zeros?

Yes, absolutely! Zeros are real numbers in your data set. If you ignore them, you're changing the problem completely. Always count every single value given.

Q: Why is my answer different from 21?

The average is not the same as the largest number! Average means the sum divided by count. Since we have 4 numbers total, $ \frac{21}{4} = 5.25 $, not 21.

Q: How do I convert 5.25 to a mixed number?

Divide: 21 ÷ 4 = 5 remainder 1. So $ 5.25 = 5\frac{1}{4} $. The whole number is 5, and the fraction part is $ \frac{1}{4} $.

Q: Can I use a calculator for this?

Absolutely! For 21 ÷ 4, a calculator gives 5.25. Just remember to convert to the required form - mixed number, decimal, or fraction as asked.

Average Calculation with Zero Values

Calculate the average

of $21,0,0,$ $0$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the average

00:04 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 (4)

00:24 Let's break down 21 into 20 plus 1

00:31 Let's break it down into whole number and remainder

00:36 Convert from whole fraction to whole number

00:42 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 $21,0,0,$ $0$ .

Step-by-step solution

To solve this problem, we'll follow these steps to find the average:

Step 1: Calculate the sum of the given numbers.
Step 2: Determine the total number of numbers provided.
Step 3: Use the formula for the average to find the solution.

Now, let's work through each step:
Step 1: Sum the numbers given: $21 + 0 + 0 + 0 = 21$ .
Step 2: Count the total number of numbers: There are $4$ numbers in total.
Step 3: Calculate the average using the formula:
$\text{Average} = \frac{\text{Sum of numbers}}{\text{Total number of numbers}} = \frac{21}{4} = 5.25$

This can be written as a mixed number: $5\frac{1}{4}$ .

Thus, the solution to the problem is $5\frac{1}{4}$ , corresponding to choice 4.

Final Answer

$5\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum of all numbers divided by count
Technique: Sum all values: 21 + 0 + 0 + 0 = 21, then divide by 4
Check: Convert decimal 5.25 to mixed number $5\frac{1}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring zero values in the count
Don't count only the non-zero numbers = wrong denominator! Counting just 21 ÷ 1 = 21 instead of 21 ÷ 4 = 5.25. Always count every single number in the sequence, including all zeros.

Practice Quiz

Test your knowledge with interactive questions

Calculate the average of $$ 10 $$ and $$ 12 $$ .

FAQ

Everything you need to know about this question

Do I really need to count the zeros?

Yes, absolutely! Zeros are real numbers in your data set. If you ignore them, you're changing the problem completely. Always count every single value given.

Why is my answer different from 21?

The average is not the same as the largest number! Average means the sum divided by count. Since we have 4 numbers total, $\frac{21}{4} = 5.25$ , not 21.

How do I convert 5.25 to a mixed number?

Divide: 21 ÷ 4 = 5 remainder 1. So $5.25 = 5\frac{1}{4}$ . The whole number is 5, and the fraction part is $\frac{1}{4}$ .

What if all the numbers were zero?

If you had 0, 0, 0, 0, the sum would be 0 and the average would be $\frac{0}{4} = 0$ . Zero is a valid average!

Can I use a calculator for this?

Absolutely! For 21 ÷ 4, a calculator gives 5.25. Just remember to convert to the required form - mixed number, decimal, or fraction as asked.

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