Calculate Average Change: Removing 11 from Sequence {1,2,3,11}

Q: How do I know if removing a number will increase or decrease the average?

Compare the number to the current average! If the number is greater than the average, removing it will decrease the average. If it's smaller than the average, removing it will increase the average.

Q: Why does removing 11 decrease the average when it's the biggest number?

Because 11 is above the average of 4.25! When you remove a value that's pulling the average up, the remaining numbers have a lower average. Think of it like removing the tallest person from a group - the average height goes down.

Q: Do I always need to calculate both averages to answer this type of question?

Not always! You can use a shortcut: just compare the number being removed to the original average. If it's bigger than the average, removal decreases it. If it's smaller, removal increases it.

Q: What if the number I'm removing equals the average exactly?

Great question! If you remove a number that equals the current average, the average will stay the same. This is because that number isn't pulling the average up or down.

Q: Can I use this same logic when adding numbers to a set?

Absolutely! It works in reverse: adding a number greater than the current average will increase the average, while adding a number less than the average will decrease it.

Average Calculations with Outlier Removal

Look at the following numbers:

$1,2,3,11$

If we remove the number 11 from the group, then what will happen to the average?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following numbers:

$1,2,3,11$

If we remove the number 11 from the group, then what will happen to the average?

Step-by-step solution

To solve this problem, we need to follow these steps:

Step 1: Determine the average of the initial set of numbers $(1, 2, 3, 11)$ .
Step 2: Determine the average of the set after removing 11 $(1, 2, 3)$ .
Step 3: Compare the averages to see the change—the average should be noted as decreasing or increasing or remaining the same.

Step 1: Calculate the average of the initial set $(1, 2, 3, 11)$ :

The sum of these numbers is $1 + 2 + 3 + 11 = 17$ .
There are 4 numbers in this set.
Thus, the average is $\frac{17}{4} = 4.25$ .

Step 2: Calculate the average of the new set $(1, 2, 3)$ :

The sum of these numbers is $1 + 2 + 3 = 6$ .
There are 3 numbers in this set.
Thus, the average is $\frac{6}{3} = 2$ .

Step 3: Compare the two averages:

The original average was $4.25$ , and the new average is $2$ . The average has decreased from $4.25$ to $2$ .

Therefore, the solution to the problem is: It will decrease.

Final Answer

It will decrease.

Key Points to Remember

Essential concepts to master this topic

Rule: Removing values above average decreases the overall average
Technique: Calculate original average: $\frac{17}{4} = 4.25$ , then new average: $\frac{6}{3} = 2$
Check: Compare values: 11 > 4.25, so removing it decreases average ✓

Common Mistakes

Avoid these frequent errors

Assuming removing any number changes average the same way
Don't think all removals decrease the average = wrong conclusion! Whether average increases or decreases depends on if the removed value is above or below the current average. Always compare the removed value to the original 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 removing a number will increase or decrease the average?

Compare the number to the current average! If the number is greater than the average, removing it will decrease the average. If it's smaller than the average, removing it will increase the average.

Why does removing 11 decrease the average when it's the biggest number?

Because 11 is above the average of 4.25! When you remove a value that's pulling the average up, the remaining numbers have a lower average. Think of it like removing the tallest person from a group - the average height goes down.

Do I always need to calculate both averages to answer this type of question?

Not always! You can use a shortcut: just compare the number being removed to the original average. If it's bigger than the average, removal decreases it. If it's smaller, removal increases it.

What if the number I'm removing equals the average exactly?

Great question! If you remove a number that equals the current average, the average will stay the same. This is because that number isn't pulling the average up or down.

Can I use this same logic when adding numbers to a set?

Absolutely! It works in reverse: adding a number greater than the current average will increase the average, while adding a number less than the average will decrease it.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Data Exploration questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime