Find the Impossible Average: Analyzing Numbers 8, 7, 5, and 10

Q: How do I know which answer is impossible?

Calculate the actual average first: $ \frac{30}{4} = 7.5 $. Any answer choice that doesn't equal 7.5 cannot be the average of these specific numbers!

Q: Why can't 12 be the average of 8, 7, 5, and 10?

Because 12 is larger than the largest number in the group (10)! An average must fall between the smallest and largest values, so 12 is impossible.

Q: Could the average ever be higher than all the numbers?

Never! The average of a group of numbers must always be between the smallest and largest numbers in that group. It's mathematically impossible for it to be outside this range.

Q: What if I calculated a different average?

Double-check your arithmetic! Add the numbers: $ 8 + 7 + 5 + 10 = 30 $, then divide by 4: $ 30 ÷ 4 = 7.5 $. The average is always unique for a given set of numbers.

Q: Do I need to check all the answer choices?

Not really! Once you calculate the actual average (7.5), you can immediately see that 12 is impossible since it's much larger than 7.5. But checking helps confirm your understanding.

Arithmetic Mean with Impossibility Analysis

Which answer cannot be the average of the group of numbers below?

$8,7,5,10$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Mark the incorrect average, without calculating

00:03 Let's place the numbers on the number line

00:10 The average should be approximately in the middle of the numbers

00:14 This option is suitable because it's approximately in the middle of the numbers

00:21 This one is also suitable

00:25 And this one too

00:29 This option cannot be the average because it's too large

00:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which answer cannot be the average of the group of numbers below?

$8,7,5,10$

Step-by-step solution

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

Step 1: Calculate the sum of the numbers.
Step 2: Find the average by dividing this sum by the number of numbers.
Step 3: Compare this calculated average to the given options to identify which cannot be the average.

Now, let's work through each step:
Step 1: Calculate the sum of the numbers: $8 + 7 + 5 + 10 = 30$ .
Step 2: Find the average by dividing the sum by the total number of numbers: $\frac{30}{4} = 7.5$ .
Step 3: Compare the calculated average to the options provided:

Option 1: $6$ - not equal to $7.5$ .
Option 2: $8$ - not equal to $7.5$ , but close enough to an integer comparison standard.
Option 3: $12$ - clearly not possible since $7.5 < 12$ .
Option 4: $9$ - not equal to $7.5$ .

Of all these options, the choice that cannot possibly be the average based on the numbers given is $12$ . Therefore, the answer is $12$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum divided by count of numbers
Technique: Calculate $\frac{8+7+5+10}{4} = \frac{30}{4} = 7.5$
Check: Compare each option to actual average of 7.5 ✓

Common Mistakes

Avoid these frequent errors

Assuming any number could be the average
Don't think all answer choices are possible = wrong elimination! The average is a fixed value determined by the given numbers. Always calculate the actual average first, then identify which option cannot equal that value.

Practice Quiz

Test your knowledge with interactive questions

If the balls below are divided so that each column in the table contains an equal number, then how many balls will there be in each column?

FAQ

Everything you need to know about this question

How do I know which answer is impossible?

Calculate the actual average first: $\frac{30}{4} = 7.5$ . Any answer choice that doesn't equal 7.5 cannot be the average of these specific numbers!

Why can't 12 be the average of 8, 7, 5, and 10?

Because 12 is larger than the largest number in the group (10)! An average must fall between the smallest and largest values, so 12 is impossible.

Could the average ever be higher than all the numbers?

Never! The average of a group of numbers must always be between the smallest and largest numbers in that group. It's mathematically impossible for it to be outside this range.

What if I calculated a different average?

Double-check your arithmetic! Add the numbers: $8 + 7 + 5 + 10 = 30$ , then divide by 4: $30 ÷ 4 = 7.5$ . The average is always unique for a given set of numbers.

Do I need to check all the answer choices?

Not really! Once you calculate the actual average (7.5), you can immediately see that 12 is impossible since it's much larger than 7.5. But checking helps confirm your understanding.

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