Calculate the Average of 5,3,7,5: Analyzing Changes with Lower Numbers

Q: Why does adding a smaller number always decrease the average?

Think of average as the balance point. When you add a number smaller than the current average (5), it pulls the balance point down. The new sum increases less than the new count, so the average drops.

Q: What happens if I add a number equal to the average?

If you add a number equal to the current average, the average stays the same! Adding 5 to our set would give us $ \frac{25}{5} = 5 $.

Q: How do I quickly check if my average calculation is correct?

Your average should be between the smallest and largest numbers in your set. Here, 3 ≤ 5 ≤ 7, so our average of 5 makes sense!

Q: Can the average be a number that's not in the original set?

Absolutely! The average represents the center value, not necessarily one of the original numbers. For example, the average of 2 and 8 is 5, even though 5 isn't in the set.

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

In basic math, mean and average are the same thing! Both refer to adding all numbers and dividing by how many numbers you have.

Average Calculations with Effect Predictions

Look at the following numbers:

$5,3,7,5$

What is the average?

If we add a number smaller than the average to the group, then how will the average change?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 First, let's find the average before and after adding a number.

00:15 We'll start by working out the average before we add anything.

00:19 To do this, we'll add up all the numbers, then divide by how many numbers there are.

00:44 That's our original average. Now, let's add the new number and see what happens.

00:49 We'll apply the average formula again to find this new average.

01:20 Now, let's compare the two averages.

01:23 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following numbers:

$5,3,7,5$

What is the average?

If we add a number smaller than the average to the group, then how will the average change?

Step-by-step solution

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

Step 1: Calculate the sum of the numbers in the group.
Step 2: Apply the formula for the average.
Step 3: Determine how adding a smaller number affects the average.

Now, let's work through each step:

Step 1: Calculate the sum of the given numbers.
The numbers are $5, 3, 7, 5$ . Their sum is:

5 + 3 + 7 + 5 = 20

Step 2: Find the average.
The formula for the average of these numbers is:

\text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} = \frac{20}{4} = 5

Therefore, the average of the numbers $5, 3, 7, 5$ is $5$ .

Step 3: Determine the effect of adding a smaller number.
If we add a number smaller than $5$ to the group, the new average will be calculated over five numbers with the new sum including this smaller number. Since this number is smaller than the current average, the overall average will decrease.

Hence, the correct answer to this problem is:
Average: 5

The average will decrease.

Final Answer

Average: 5

The average will decrease

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum of numbers divided by count
Technique: Sum: 5+3+7+5=20, then divide 20÷4=5
Check: Adding smaller number decreases average since it pulls down ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count all numbers when calculating average
Don't divide by 3 when you have 4 numbers = wrong average! Students often miscount the total numbers in the set. Always count carefully: 5,3,7,5 has exactly 4 numbers, so divide the sum by 4.

Practice Quiz

Test your knowledge with interactive questions

Calculate the average of $$ 11 $$ and $$ 7 $$ .

FAQ

Everything you need to know about this question

Why does adding a smaller number always decrease the average?

Think of average as the balance point. When you add a number smaller than the current average (5), it pulls the balance point down. The new sum increases less than the new count, so the average drops.

What happens if I add a number equal to the average?

If you add a number equal to the current average, the average stays the same! Adding 5 to our set would give us $\frac{25}{5} = 5$ .

How do I quickly check if my average calculation is correct?

Your average should be between the smallest and largest numbers in your set. Here, 3 ≤ 5 ≤ 7, so our average of 5 makes sense!

Can the average be a number that's not in the original set?

Absolutely! The average represents the center value, not necessarily one of the original numbers. For example, the average of 2 and 8 is 5, even though 5 isn't in the set.

What's the difference between mean and average?

In basic math, mean and average are the same thing! Both refer to adding all numbers and dividing by how many numbers you have.

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