Calculate Average Change: Adding 10 to Numbers 2,3,4,5

Average Calculation with Additional Data

Look at the following numbers:

2,3,4,5 2,3,4,5

If we add the number 10 to the group, then what will happen to the average?

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1

Understand the problem

Look at the following numbers:

2,3,4,5 2,3,4,5

If we add the number 10 to the group, then what will happen to the average?

2

Step-by-step solution

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

  • Step 1: Calculate the sum and average of the original numbers.
  • Step 2: Add the number 10 to the original list and calculate the new sum and average.
  • Step 3: Compare the two averages to determine if there is an increase, decrease, or no change.

Now, let's work through each step:

Step 1: Calculate the sum and average of the original numbers (2, 3, 4, 5).
Sum = 2+3+4+5=142 + 3 + 4 + 5 = 14
Average = 144=3.5\frac{14}{4} = 3.5

Step 2: Include the number 10 in the group.
New sum = 14+10=2414 + 10 = 24
New average = 245=4.8\frac{24}{5} = 4.8

Step 3: Compare the averages.
Original average was 3.5, and the new average is 4.8.

The new average (4.8) is greater than the original average (3.5), which means the average will increase.

Therefore, the correct choice is: It will increase.

3

Final Answer

It will increase.

Key Points to Remember

Essential concepts to master this topic
  • Rule: Adding data above the current average increases the overall average
  • Technique: Compare new value to current average: 10 > 3.5, so average increases
  • Check: Calculate both averages: 3.5 → 4.8 shows increase ✓

Common Mistakes

Avoid these frequent errors
  • Assuming the average always increases when adding any number
    Don't think adding any number increases the average = wrong conclusion! If you add a number below the current average (like adding 1 to our example), the average decreases. Always compare the new number to the current average first.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

How do I know if adding a number will change the average?

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Compare the new number to the current average! If it's higher than the average, the average increases. If it's lower, the average decreases. If it equals the average, no change occurs.

Do I always need to calculate both averages?

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For verification, yes! But you can predict the direction of change by comparing the new number to the current average. In our case, 10 > 3.5, so we know the average will increase before calculating.

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

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The average stays the same! Adding a value equal to the current average doesn't change it. For example, adding 3.5 to our set {2,3,4,5} keeps the average at 3.5.

Why does adding 10 make such a big difference to the average?

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Because 10 is much larger than our current average of 3.5! The bigger the difference between the new number and current average, the more dramatic the change. Adding 4 would barely increase it, but adding 10 creates a big jump.

Is there a shortcut to find the new average?

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Yes! New average = old sum+new numberold count+1 \frac{\text{old sum} + \text{new number}}{\text{old count} + 1} . So: 14+104+1=245=4.8 \frac{14 + 10}{4 + 1} = \frac{24}{5} = 4.8

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