Calculate Average Change: Removing One 10 from (10,10,10,10)

Q: Why doesn't removing a 10 change the average when all numbers are 10?

When all numbers are identical, they all equal the average! Removing one doesn't change this because you're taking away exactly what the average was.

Q: What would happen if I removed a different number instead?

You can't remove a different number because all the numbers in this set are 10! Every number you could remove equals the average, so the result is always the same.

Q: Does this rule work with other identical numbers too?

Yes! Whether you have five 7s, three 15s, or ten 2s, removing one identical number never changes the average. The average of identical numbers is always that number.

Q: How is this different from removing numbers that aren't all the same?

Great question! If numbers are different, removing one usually changes the average. For example, removing 5 from (3,5,7) changes the average from 5 to 5. But identical numbers? No change!

Q: Is there a quick way to spot this without calculating?

Yes! When you see all identical numbers, you know immediately that the average equals that number, and removing one won't change it. No calculation needed!

Average Calculations with Identical Data Values

Look at the following numbers:

$10,10,10,10$

If we remove the number 10 once from the group, what will happen to the average?

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Step-by-step written solution

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Understand the problem

Look at the following numbers:

$10,10,10,10$

If we remove the number 10 once from the group, what will happen to the average?

Step-by-step solution

To solve this problem, we need to calculate the average of the numbers before and after removing one 10.

Initially, we have the numbers $10, 10, 10, 10$ .

Calculation of the initial average:
- Sum of numbers: $10 + 10 + 10 + 10 = 40$
- Number of numbers: 4
- Average: $\frac{40}{4} = 10$

Now, we remove one of the 10s, leaving the numbers $10, 10, 10$ .

Calculation of the new average:
- Sum of numbers: $10 + 10 + 10 = 30$
- Number of numbers: 3
- Average: $\frac{30}{3} = 10$

We see that in both cases, the average is 10. Thus, removing one 10 does not change the average of the numbers.

Therefore, the average will remain the same.

Hence, the correct choice is: It will remain the same.

Final Answer

It will remain the same.

Key Points to Remember

Essential concepts to master this topic

Rule: When all numbers are identical, the average equals that number
Technique: Calculate $\frac{40}{4} = 10$ and $\frac{30}{3} = 10$
Check: Both original and reduced sets have average 10 ✓

Common Mistakes

Avoid these frequent errors

Assuming removing a number always changes the average
Don't think removing any number must change the average = wrong reasoning! This only applies when numbers differ from the mean. Always check if the removed value equals 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

Why doesn't removing a 10 change the average when all numbers are 10?

When all numbers are identical, they all equal the average! Removing one doesn't change this because you're taking away exactly what the average was.

What would happen if I removed a different number instead?

You can't remove a different number because all the numbers in this set are 10! Every number you could remove equals the average, so the result is always the same.

Does this rule work with other identical numbers too?

Yes! Whether you have five 7s, three 15s, or ten 2s, removing one identical number never changes the average. The average of identical numbers is always that number.

How is this different from removing numbers that aren't all the same?

Great question! If numbers are different, removing one usually changes the average. For example, removing 5 from (3,5,7) changes the average from 5 to 5. But identical numbers? No change!

Is there a quick way to spot this without calculating?

Yes! When you see all identical numbers, you know immediately that the average equals that number, and removing one won't change it. No calculation needed!

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