Find Groups with Mean = 6: Average Value Selection Problem

Average Calculations with Multiple Choice Verification

Choose the group of numbers of which 6 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 6
00:03 To calculate the average, we sum up and divide by the number of occurrences
00:10 We'll use the formula for calculating average to find the mean
00:15 This is the average, now let's move to the next group
00:18 We'll use the formula for calculating average to find the mean
00:25 This is the average, now let's move to the next group
00:30 In a group where all numbers are identical, the average is that number
00:35 This is the average, now let's move to the next group
00:39 We'll use the formula for calculating average to find the mean
00:47 This is the average
00:50 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 6 is the average.

2

Step-by-step solution

To solve this problem, we will apply the formula for the average. We will proceed by evaluating each choice to identify which group has an average of 6.

The average for a group of numbers is calculated as:

Average=Sum of valuesNumber of values \text{Average} = \frac{\text{Sum of values}}{\text{Number of values}}

Now, let's calculate and analyze:

  • Choice 1: 1,2,31,2,3
    Calculate the sum: 1+2+3=61 + 2 + 3 = 6
    Number of values: 3
    Average: 63=2\frac{6}{3} = 2

  • Choice 2: 3,3,33,3,3
    Calculate the sum: 3+3+3=93 + 3 + 3 = 9
    Number of values: 3
    Average: 93=3\frac{9}{3} = 3

  • Choice 3: 6,0,06,0,0
    Calculate the sum: 6+0+0=66 + 0 + 0 = 6
    Number of values: 3
    Average: 63=2\frac{6}{3} = 2

  • Choice 4: 6,8,46,8,4
    Calculate the sum: 6+8+4=186 + 8 + 4 = 18
    Number of values: 3
    Average: 183=6\frac{18}{3} = 6

Thus, the group of numbers with an average of 6 is 6,8,46,8,4.

3

Final Answer

6,8,4 6,8,4

Key Points to Remember

Essential concepts to master this topic
  • Formula: Average equals sum of all values divided by count
  • Method: Calculate 6+8+43=183=6 \frac{6+8+4}{3} = \frac{18}{3} = 6
  • Check: Test each option systematically until one equals target average ✓

Common Mistakes

Avoid these frequent errors
  • Assuming equal numbers must have the target average
    Don't think numbers like 6,6,6 automatically give average 6 when other values are present = wrong logic! Just because one number matches the target doesn't mean the whole group does. Always calculate the actual sum divided by count for each option.

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 all the numbers need to be close to 6 for the average to be 6?

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No! Numbers can vary widely and still average to 6. For example, 2, 4, and 12 average to 183=6 \frac{18}{3} = 6 even though 12 is much larger than 6.

What if I get a decimal when calculating the average?

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That's normal! If your calculation gives a decimal like 2.5, that's the actual average. Only whole number averages will match our target of 6 in this problem.

Is there a faster way than calculating all four options?

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You can use logic: if you need average 6 with 3 numbers, the sum must be 6×3=18 6 \times 3 = 18 . Look for the group that adds to 18!

Can the average be larger than all the numbers in the group?

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Never! The average must always fall between the smallest and largest values in your group. If all numbers are less than 6, the average cannot be 6.

What if two groups both have the right average?

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In multiple choice questions, only one answer should be correct. Double-check your arithmetic if you think you found two correct answers!

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