Calculate the Mean of 10, 12, 8: Exploring Average Changes

Q: Why does adding a number larger than the mean always increase the average?

Think of the mean as a balance point. When you add a number above this point, it pulls the balance upward, making the new average higher than before.

Q: What would happen if I added a number smaller than 10?

The average would decrease! Adding any number below the current mean pulls the average down. For example, adding 5 would give us $ \frac{35}{4} = 8.75 $.

Q: Does it matter how much larger the new number is?

Yes! The further above the mean, the bigger the increase. Adding 11 increases the mean slightly, but adding 20 would increase it much more.

Q: How do I calculate the mean of any set of numbers?

Follow these steps: Step 1: Add all the numbers togetherStep 2: Count how many numbers you haveStep 3: Divide the sum by the count

Q: What if I add a number exactly equal to the current mean?

The mean stays exactly the same! Adding 10 to our group would give $ \frac{40}{4} = 10 $, keeping the average unchanged.

Q: Is there a quick way to predict how the mean will change?

Compare the new number to the current mean: If new number > mean, average goes up. If new number

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the average before and after adding the number

00:03 Let's start by calculating the average before adding the number

00:14 To calculate an average, we'll sum and divide by the number of occurrences

00:32 This is the original average, now let's add the number and check

00:39 We'll use the average formula to find the new average

00:59 Let's compare the averages

01:07 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Look at the following numbers:

$10,12,8$

What is the average?

If we add a number larger than the average to the group (e.g. 11), then how will the average change?

2

Step-by-step solution

To solve this problem, we'll determine the initial average of the numbers provided and address the change in the average when a new number is added:

Step 1: Calculate the initial average.
Step 2: Add the new number to recalculate the average.
Step 3: Compare the old and new averages.

Step 1: Calculate the initial average of 10, 12, and 8:
- First, find the sum of the numbers: $10 + 12 + 8 = 30$ .
- There are 3 numbers, so divide the sum by 3 to get the average: $\frac{30}{3} = 10$ .

Step 2: Add the number 11 (which is larger than the initial average) to the group and recalculate the average:
- The new sum is $30 + 11 = 41$ with a total of 4 numbers.
- The new average becomes $\frac{41}{4} = 10.25$ .

Step 3: Compare the averages:
- The initial average is 10.
- The new average is 10.25, which is higher than 10.

Therefore, adding a number larger than the initial average results in an increased average. So, the average will increase when 11 is added.

The correct answer to the question is: Average 10, the average will increase.

3

Final Answer

Average 10, the average will increase

Key Points to Remember

Essential concepts to master this topic

Mean Formula: Add all numbers then divide by count
Technique: Sum 10 + 12 + 8 = 30, then divide by 3 numbers
Check: New mean $\frac{41}{4} = 10.25$ > original mean 10 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to update the count when adding new data
Don't divide the new sum by the old count = wrong average! When you add 11 to get sum 41, you now have 4 numbers, not 3. Always update both the sum AND the count when adding data points.

Practice Quiz

Test your knowledge with interactive questions

Calculate the average of $$ 11 $$ and $$ 7 $$ .

FAQ

Everything you need to know about this question

Why does adding a number larger than the mean always increase the average?

+

Think of the mean as a balance point. When you add a number above this point, it pulls the balance upward, making the new average higher than before.

What would happen if I added a number smaller than 10?

+

The average would decrease! Adding any number below the current mean pulls the average down. For example, adding 5 would give us $\frac{35}{4} = 8.75$ .

Does it matter how much larger the new number is?

+

Yes! The further above the mean, the bigger the increase. Adding 11 increases the mean slightly, but adding 20 would increase it much more.

How do I calculate the mean of any set of numbers?

+

Follow these steps:

Step 1: Add all the numbers together
Step 2: Count how many numbers you have
Step 3: Divide the sum by the count

What if I add a number exactly equal to the current mean?

+

The mean stays exactly the same! Adding 10 to our group would give $\frac{40}{4} = 10$ , keeping the average unchanged.

Is there a quick way to predict how the mean will change?

+

Compare the new number to the current mean: If new number > mean, average goes up. If new number < mean, average goes down. If new number = mean, average stays the same.

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Calculate the Mean of 10, 12, 8: Exploring Average Changes

Mean Calculation with Data Addition Effects

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