Calculate Average: Finding Mean Before and After Adding 2 to {10,12,8}

Q: Why does the mean change when I add 2 to each number?

When you add 2 to each of the 3 numbers, you're adding 6 total to the sum (2 × 3 = 6). Since the mean is the sum divided by 3, adding 6 to the sum increases the mean by $ \frac{6}{3} = 2 $!

Q: Is there a shortcut instead of calculating both means separately?

Yes! When you add the same constant to every value, just add that constant to the original mean. Original mean 10 + constant 2 = new mean 12. This works for any transformation!

Q: Does this work with multiplication too?

Not quite the same way. If you multiply each value by 2, the new mean will be the original mean times 2. But with addition/subtraction, you add/subtract that same amount to the mean.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the average before and after changing the group

00:03 Let's start by calculating the average before changing the group

00:08 To calculate the average, we'll sum and divide by the number of occurrences

00:22 This is the original average, now let's change the group and check

00:34 We'll use the average formula to find the new average

00:53 Let's compare the averages

00:57 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 following numbers:

$10,12,8$

What is the average?

If each number is increased by 2, we get the following:

$12,14,10$

What is the average of this new group of numbers?

2

Step-by-step solution

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

Step 1: Calculate the average of the original numbers.
Step 2: Calculate the average of the increased numbers.
Step 3: Compare the averages.

Now, let's work through each step:

Step 1: The original numbers are 10, 12, and 8.
Calculate their sum: $10 + 12 + 8 = 30$ .
Divide the sum by the number of numbers: $\frac{30}{3} = 10$ .
Therefore, the average of the original numbers is $10$ .

Step 2: The increased numbers are 12, 14, and 10.
Calculate their sum: $12 + 14 + 10 = 36$ .
Divide the sum by the number of numbers: $\frac{36}{3} = 12$ .
Therefore, the average of the increased numbers is $12$ .

Step 3: Compare the averages.
The average increased from $10$ to $12$ , which is an increase by $2$ .

Conclusion: Since the average increases by $2$ , the answer is that the average of the new group of numbers is $12$ , and it increases by $2$ from the original average.

Therefore, the correct answer is choice 1:
Average = 10
The average will increase by 2.

3

Final Answer

Average = 10
The average will increase by 2.

Key Points to Remember

Essential concepts to master this topic

Formula: Mean equals sum of values divided by count
Technique: When adding 2 to each value: $\frac{30+6}{3} = 12$
Check: Original mean 10 plus constant 2 equals new mean 12 ✓

Common Mistakes

Avoid these frequent errors

Thinking the mean stays the same when adding constants
Don't assume adding the same number to each value leaves the mean unchanged = wrong answer! This ignores how constants affect the sum. Always remember: when you add the same constant to every data value, the mean increases by exactly that constant.

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 the mean change when I add 2 to each number?

+

When you add 2 to each of the 3 numbers, you're adding 6 total to the sum (2 × 3 = 6). Since the mean is the sum divided by 3, adding 6 to the sum increases the mean by $\frac{6}{3} = 2$ !

Is there a shortcut instead of calculating both means separately?

+

Yes! When you add the same constant to every value, just add that constant to the original mean. Original mean 10 + constant 2 = new mean 12. This works for any transformation!

What if I subtract the same number from each value?

+

The same rule applies! If you subtract 3 from each number, the new mean will be the original mean minus 3. The mean changes by exactly the same amount you add or subtract.

Does this work with multiplication too?

+

Not quite the same way. If you multiply each value by 2, the new mean will be the original mean times 2. But with addition/subtraction, you add/subtract that same amount to the mean.

How can I check my answer without doing all the calculations?

+

Use the transformation rule! Start with your original mean, then apply the same operation. Original mean 10, add 2 to get 12. Then verify: $\frac{12+14+10}{3} = \frac{36}{3} = 12$ ✓

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Calculate Average: Finding Mean Before and After Adding 2 to {10,12,8}

Mean Calculation with Uniform Data Transformation

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