Calculate the Average: Finding Mean of 4 Numbers with Sum 20

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

The sum is what you get when you add all numbers together (20 in this problem). The average is the sum divided by how many numbers you have, giving you the typical value (5 in this case).

Q: Do I need to know what the actual 4 numbers are?

No! You only need the sum (20) and count (4 numbers). The average formula works even when you don't know the individual numbers: $ \frac{20}{4} = 5 $.

Q: Could the 4 numbers be 2, 3, 7, and 8?

Let's check: 2 + 3 + 7 + 8 = 20 ✓ Yes! Any four numbers that add up to 20 will have an average of 5.

Q: What if I accidentally divide 4 by 20?

You'd get 0.2, which is way too small! Remember: Average = Sum ÷ Count, so it's always the bigger number (sum) divided by the smaller number (count).

Average Formula with Given Sum

What is the average of four numbers that have a sum of 20?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the average of these numbers.

00:07 To get the average, we first add up all the numbers. Then we divide by how many numbers we have.

00:13 We simply put in the total sum and divide it by the total number of numbers.

00:19 And that's how we solve this, finding the average easily.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the average of four numbers that have a sum of 20?

Step-by-step solution

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

Step 1: Identify the number of values for which we are calculating the average. In this case, it is $4$ .
Step 2: Identify the given total sum, which is $20$ .
Step 3: Use the average formula to calculate: Average = $\frac{\text{Sum}}{\text{Total Count}}$ .

Now, let's work through each step:
Step 1: We know that we are dealing with $4$ numbers.
Step 2: The total sum of these numbers is given as $20$ .
Step 3: Using the formula for the average, we calculate:
$\text{Average} = \frac{20}{4} = 5$ .

Therefore, the solution to the problem is $5$ .

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals total sum divided by count of numbers
Technique: Set up $\frac{20}{4} = 5$ using given values
Check: Verify that 4 numbers averaging 5 sum to 20 ✓

Common Mistakes

Avoid these frequent errors

Confusing sum with average
Don't give 20 as the answer just because it's the sum! The sum is the total of all numbers added together, while average divides that sum by how many numbers there are. Always divide the sum by the count to find the average.

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

What's the difference between sum and average?

The sum is what you get when you add all numbers together (20 in this problem). The average is the sum divided by how many numbers you have, giving you the typical value (5 in this case).

Do I need to know what the actual 4 numbers are?

No! You only need the sum (20) and count (4 numbers). The average formula works even when you don't know the individual numbers: $\frac{20}{4} = 5$ .

Could the 4 numbers be 2, 3, 7, and 8?

Let's check: 2 + 3 + 7 + 8 = 20 ✓ Yes! Any four numbers that add up to 20 will have an average of 5.

What if I accidentally divide 4 by 20?

You'd get 0.2, which is way too small! Remember: Average = Sum ÷ Count, so it's always the bigger number (sum) divided by the smaller number (count).

How can I remember the average formula?

Think of it like sharing equally: if 4 people share 20 cookies, each person gets $\frac{20}{4} = 5$ cookies. That's the average!

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