Calculate Average Change: Adding 7 to Sequence (7,7,7,7)

Q: Why doesn't the average change when I add another 7?

The average stays the same because you're adding a number equal to the current average. Since $ 7 = 7 $, it doesn't pull the average up or down!

Q: What would happen if I added a different number like 8?

If you added 8 instead, the average would increase because 8 is greater than the current average of 7. The new average would be $ \frac{28 + 8}{5} = 7.2 $.

Q: How can I predict if the average will change without calculating?

Quick rule: Compare the new number to the current average. If it's higher, average increases. If it's lower, average decreases. If it's equal, average stays the same!

Q: What if all numbers in the sequence are the same?

When all numbers are identical, the average will always equal that number. Adding more of the same value keeps this pattern: $ \frac{7n}{n} = 7 $ for any number of 7's.

Average Calculation with Identical Values

Look at the following numbers:

$7,7,7,7$

If the number 7 is added to the group, 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:

$7,7,7,7$

If the number 7 is added to the group, how will the average change?

Step-by-step solution

To solve this problem, let's calculate the average of the numbers before and after introducing an additional $7$ .

Initially, we have four numbers: $7, 7, 7, 7$ .

Step 1: Calculate the sum of these numbers.
$7 + 7 + 7 + 7 = 28$ .
Step 2: Calculate the initial average.
$\frac{28}{4} = 7$ .

Now, we add another $7$ to the group, resulting in five numbers: $7, 7, 7, 7, 7$ .

Step 3: Calculate the new sum.
$28 + 7 = 35$ .
Step 4: Calculate the new average.
$\frac{35}{5} = 7$ .

Both the initial average and the new average are $7$ . Therefore, the average remains unchanged.

Based on this analysis, the correct choice is:

It will remain the same.

Therefore, the solution to the problem is it will remain the same..

Final Answer

It will remain the same.

Key Points to Remember

Essential concepts to master this topic

Rule: Adding the same value as current average keeps average unchanged
Technique: Compare new value to current average: $7 = 7$
Check: Calculate both averages: $\frac{28}{4} = \frac{35}{5} = 7$ ✓

Common Mistakes

Avoid these frequent errors

Assuming adding any number changes the average
Don't think that adding more numbers always changes the average = wrong conclusion! The average only changes when you add a value different from the current average. Always compare the new value 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 doesn't the average change when I add another 7?

The average stays the same because you're adding a number equal to the current average. Since $7 = 7$ , it doesn't pull the average up or down!

What would happen if I added a different number like 8?

If you added 8 instead, the average would increase because 8 is greater than the current average of 7. The new average would be $\frac{28 + 8}{5} = 7.2$ .

How can I predict if the average will change without calculating?

Quick rule: Compare the new number to the current average. If it's higher, average increases. If it's lower, average decreases. If it's equal, average stays the same!

Do I always need to recalculate the entire average?

Not always! If the new value equals the current average, you can immediately say the average won't change. Only recalculate when you need to find the exact new value.

What if all numbers in the sequence are the same?

When all numbers are identical, the average will always equal that number. Adding more of the same value keeps this pattern: $\frac{7n}{n} = 7$ for any number of 7's.

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