Find Number Groups with Mean Value of 2: Average Calculation

Average Calculation with Multiple Choice Analysis

Choose the group of numbers of which 2 is the average.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the group with an average of 2
00:03 To calculate the average, we sum and divide by the number of occurrences
00:09 In a group where all numbers are identical, the average is that number
00:16 Let's verify the average using the formula for calculating averages
00:26 This is the average, now let's move to the next group
00:31 We'll use the formula for calculating averages to find the average
00:37 This is the average, now let's move to the next group
00:41 In a group where all numbers are identical, the average is that number
00:51 Let's verify the average using the formula for calculating averages
00:55 This is the average, now let's move to the next group
01:10 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

Choose the group of numbers of which 2 is the average.

2

Step-by-step solution

To solve this problem, we need to compute the average for each group of numbers provided in the options and check which group has an average of 2.

Step 1: Calculate the average for each group:

  • Choice 1: 1,21, 2
    - Sum = 1+2=31 + 2 = 3
    - Count = 22
    - Average = 32=1.5\frac{3}{2} = 1.5
  • Choice 2: 3,33, 3
    - Sum = 3+3=63 + 3 = 6
    - Count = 22
    - Average = 62=3\frac{6}{2} = 3
  • Choice 3: 2,02, 0
    - Sum = 2+0=22 + 0 = 2
    - Count = 22
    - Average = 22=1\frac{2}{2} = 1
  • Choice 4: 2,2,2,22, 2, 2, 2
    - Sum = 2+2+2+2=82 + 2 + 2 + 2 = 8
    - Count = 44
    - Average = 84=2\frac{8}{4} = 2

Step 2: Identify the correct choice.
From the calculations above, the only group that has an average of 2 is Choice 4 (2,2,2,22, 2, 2, 2).

Therefore, the correct group of numbers with an average of 2 is 2,2,2,22, 2, 2, 2.

3

Final Answer

2,2,2,2 2,2,2,2

Key Points to Remember

Essential concepts to master this topic
  • Average Formula: Sum of all numbers divided by count of numbers
  • Method: Calculate 2+2+2+24=84=2 \frac{2+2+2+2}{4} = \frac{8}{4} = 2 for each option
  • Verification: Only the group where all calculations equal 2 is correct ✓

Common Mistakes

Avoid these frequent errors
  • Adding numbers without dividing by count
    Don't just add the numbers and stop = wrong answer! This gives you the sum, not the average. Always divide the sum by how many numbers you counted.

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

Do I have to check all the answer choices?

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Yes! Calculate the average for each group to be certain. Even if you find one that equals 2, check the others to make sure there's only one correct answer.

What if two groups both have an average of 2?

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Both would be mathematically correct! However, in multiple choice questions, typically only one option will have the target average of 2.

Why does (2,2,2,2) have an average of 2?

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When all numbers in a group are the same, the average equals that number. Since all four numbers are 2, the average is 2!

Can I use mental math instead of writing it out?

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For simple cases like (1,2) (1,2) , mental math works: 1+2=3, divided by 2 = 1.5. But writing steps helps avoid errors with larger groups.

What if the numbers include decimals or fractions?

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The same formula applies! Add all numbers (including decimals/fractions) and divide by the count. Just be extra careful with your arithmetic.

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