Find Number Groups with Average of 10: Selection Challenge

Average Calculation with Multiple Values

Choose the group of numbers of which 10 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 10
00:03 To calculate the average, we'll sum and divide by the number of occurrences
00:18 This is the average, now let's move to the next group
00:23 We'll use the formula for calculating average to find the mean
00:33 This is the average, now let's move to the next group
00:37 We'll use the formula for calculating average to find the mean
00:45 This is the average, now let's move to the next group
00:50 We'll use the formula for calculating average to find the mean
01:00 This is the average
01:04 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 10 is the average.

2

Step-by-step solution

To solve the problem of determining which group of numbers has an average of 10, we will evaluate each provided choice:

  • Choice 1: 10,12,11 10, 12, 11
    Sum = 10+12+11=33 10 + 12 + 11 = 33
    Number of elements = 3
    Average = 333=11 \frac{33}{3} = 11
  • Choice 2: 8,10 8, 10
    Sum = 8+10=18 8 + 10 = 18
    Number of elements = 2
    Average = 182=9 \frac{18}{2} = 9
  • Choice 3: 10,0 10, 0
    Sum = 10+0=10 10 + 0 = 10
    Number of elements = 2
    Average = 102=5 \frac{10}{2} = 5
  • Choice 4: 40,0,0,0 40, 0, 0, 0
    Sum = 40+0+0+0=40 40 + 0 + 0 + 0 = 40
    Number of elements = 4
    Average = 404=10 \frac{40}{4} = 10

After evaluating all the choices, we find that Choice 4: 40,0,0,0 40, 0, 0, 0 achieves an average of 10.

Therefore, the solution to the problem is 40,0,0,0 40, 0, 0, 0 .

3

Final Answer

40,0,0,0 40,0,0,0

Key Points to Remember

Essential concepts to master this topic
  • Formula: Average equals sum of all values divided by count
  • Technique: Calculate 40+0+0+04=404=10 \frac{40+0+0+0}{4} = \frac{40}{4} = 10
  • Check: Verify each option by computing sum ÷ count = target average ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to count all values including zeros
    Don't ignore zeros when counting elements = wrong denominator! Students often count (40, 0, 0, 0) as just 1 value instead of 4, getting 40÷1 = 40 instead of 10. Always count every single number in the group, including all zeros.

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 need to include zeros when calculating the average?

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Yes, absolutely! Zeros are real numbers that affect both the sum and the count. In (40, 0, 0, 0), all four numbers matter for the calculation.

Why isn't (10, 12, 11) correct if 10 is in the group?

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Having the number 10 in a group doesn't guarantee the average is 10! The average of (10, 12, 11) is 333=11 \frac{33}{3} = 11 , not 10.

How can a group with such different numbers have an average of 10?

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The large number (40) gets balanced out by multiple zeros and divided by the total count. Think of it as distributing 40 equally among 4 positions: each gets 10.

Is there a shortcut to check if the average is 10?

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Yes! Multiply 10 by the number of values to get the required sum. For 4 numbers: 10×4=40 10 \times 4 = 40 . Then see which group adds up to exactly 40.

What if I get confused by all the calculations?

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Take it step by step: 1) Add all numbers, 2) Count how many numbers, 3) Divide sum by count. Write each step clearly!

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