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

Look at the following numbers:

5,3,7,5 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
1

Understand the problem

Look at the following numbers:

5,3,7,5 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?

2

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 5,3,7,55, 3, 7, 5. Their sum is:

5+3+7+5=20 5 + 3 + 7 + 5 = 20 .

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

Average=Sum of numbersCount of numbers=204=5 \text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} = \frac{20}{4} = 5 .

Therefore, the average of the numbers 5,3,7,55, 3, 7, 5 is 55.

Step 3: Determine the effect of adding a smaller number.
If we add a number smaller than 55 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.

3

Final Answer

Average: 5

The average will decrease

Practice Quiz

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Calculate the average of \( 10 \) and \( 12 \).

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