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

Question

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?

Video Solution

Solution Steps

00:00 Find the average before and after adding the number
00:04 Let's start by calculating the average before adding the number
00:08 To calculate the average, we'll sum and divide by the number of occurrences
00:33 This is the original average, now let's add the number and check
00:38 We'll use the average formula to find the new average
01:09 Let's compare the averages
01:12 And this is the solution to the question

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.

Answer

Average: 5

The average will decrease