Calculate the Average Change: Adding 1 to the Set {2,3,4,5}

Q: Why does adding a number sometimes decrease the average?

The average decreases when you add a number that's below the current average. Since 1 is less than 3.5, it pulls the average down to 3!

Q: How can I predict if the average will go up or down?

Compare the new number to the current average: If it's higher, average goes up. If it's lower, average goes down. If equal, average stays the same.

Q: Do I always need to calculate both averages completely?

For quick checks, compare first! Since 1

Q: What if I add multiple numbers at once?

The same principle applies! If the average of the new numbers is below the current average, the overall average decreases.

Q: Why does the calculation use sum divided by count?

That's the definition of average! Add all values together, then divide by how many values you have. It gives you the 'typical' or middle value.

Average Calculations with Adding Elements

Look at the following numbers:

$2,3,4,5$

If we add the number 1 to the group, then how will the average change?

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Step-by-step written solution

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Understand the problem

Look at the following numbers:

$2,3,4,5$

If we add the number 1 to the group, then how will the average change?

Step-by-step solution

To solve this problem, we'll begin by calculating the average of the original group of numbers ( $2, 3, 4, 5$ ):

1. Calculate the sum of the original group: $2 + 3 + 4 + 5 = 14$ .

2. Determine the number of elements in the original group: $4$ .

3. Calculate the average of the original group: $\frac{14}{4} = 3.5$ .

Next, we'll calculate the average after adding the number $1$ to the group, forming the new group ( $1, 2, 3, 4, 5$ ):

1. Calculate the sum of the new group: $1 + 2 + 3 + 4 + 5 = 15$ .

2. Determine the number of elements in the new group: $5$ .

3. Calculate the average of the new group: $\frac{15}{5} = 3$ .

Finally, compare the two averages:

The average of the original group is $3.5$ , while the average of the new group is $3$ .

The average decreases when the number 1 is added to the group.

Therefore, the solution to the problem is that the average will decrease.

Final Answer

It will decrease.

Key Points to Remember

Essential concepts to master this topic

Rule: Adding values below current average decreases overall average
Technique: Original average 3.5, adding 1 gives new average 15÷5 = 3
Check: Compare old average 3.5 to new average 3: decrease confirmed ✓

Common Mistakes

Avoid these frequent errors

Assuming adding any number increases the average
Don't think adding more numbers always increases the average = wrong conclusion! Adding numbers below the current average pulls it down. Always compare the new number to the existing 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

Why does adding a number sometimes decrease the average?

The average decreases when you add a number that's below the current average. Since 1 is less than 3.5, it pulls the average down to 3!

How can I predict if the average will go up or down?

Compare the new number to the current average: If it's higher, average goes up. If it's lower, average goes down. If equal, average stays the same.

Do I always need to calculate both averages completely?

For quick checks, compare first! Since 1 < 3.5, you know the average will decrease. But always calculate both to find the exact change.

What if I add multiple numbers at once?

The same principle applies! If the average of the new numbers is below the current average, the overall average decreases.

Why does the calculation use sum divided by count?

That's the definition of average! Add all values together, then divide by how many values you have. It gives you the 'typical' or middle value.

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