Find Number Groups with Mean = 4: Average Value Problem

Mean Calculation with Multiple Choice Selection

Choose the group of numbers of which 4 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 4
00:03 To calculate the average, we'll sum and divide by the number of occurrences
00:14 This is the average, now let's move to the next group
00:31 This is the average, now let's move to the next group
00:43 This is the average, note that it's 4, now let's move to the next group
00:50 In a group where all numbers are identical, the average is that number
00:53 Let's verify the average using the formula for calculating the average
01:05 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 4 is the average.

2

Step-by-step solution

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

  • Calculate the average for each group of numbers provided in the choices.
  • Identify the group whose average equals 4.

Let's apply these steps to each choice:

Choice 1: 2,22, 2

Sum=2+2=4\text{Sum} = 2 + 2 = 4
Count=2\text{Count} = 2
Average=42=2\text{Average} = \frac{4}{2} = 2

Choice 2: 6,3,36, 3, 3

Sum=6+3+3=12\text{Sum} = 6 + 3 + 3 = 12
Count=3\text{Count} = 3
Average=123=4\text{Average} = \frac{12}{3} = 4

Choice 3: 6,4,56, 4, 5

Sum=6+4+5=15\text{Sum} = 6 + 4 + 5 = 15
Count=3\text{Count} = 3
Average=153=5\text{Average} = \frac{15}{3} = 5

Choice 4: 4,0,04, 0, 0

Sum=4+0+0=4\text{Sum} = 4 + 0 + 0 = 4
Count=3\text{Count} = 3
Average=431.33\text{Average} = \frac{4}{3} \approx 1.33

Upon examining these calculations, the group 6,3,36, 3, 3 (Choice 2) has an average of 4, which satisfies the condition given in the problem.

Therefore, the solution to the problem is 6,3,3 6, 3, 3 .

3

Final Answer

6,3,3 6,3,3

Key Points to Remember

Essential concepts to master this topic
  • Formula: Average equals sum of all values divided by count
  • Technique: Calculate each choice: 6+3+33=123=4 \frac{6+3+3}{3} = \frac{12}{3} = 4
  • Check: Verify the sum equals mean times count: 4 × 3 = 12 ✓

Common Mistakes

Avoid these frequent errors
  • Only checking if one number equals the target mean
    Don't assume that if 4 appears in a group, the average is 4! One number doesn't determine the mean. Always calculate the sum divided by count for the entire group.

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

Why isn't (4, 0, 0) correct since it contains 4?

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The average isn't determined by just one number in the group! You need 4+0+03=431.33 \frac{4+0+0}{3} = \frac{4}{3} ≈ 1.33 , not 4.

How do I quickly check if a group has the right average?

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Use this shortcut: Sum should equal mean × count. For mean = 4 with 3 numbers, sum must equal 12. Only (6,3,3) gives 6+3+3=12!

What if I get a decimal average instead of a whole number?

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That's normal! Averages can be decimals. For example, 43=1.3 \frac{4}{3} = 1.\overline{3} is a valid average, just not the one we want here.

Can numbers in a group repeat?

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Yes! Notice that (6,3,3) has two 3's and (2,2) has two 2's. Repeated values are completely fine when calculating averages.

Is there a pattern to find groups with a specific mean?

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Yes! If you want mean = 4, think of numbers that balance around 4. Like 6 is 2 above 4, so you need 2 numbers that are 1 below 4 each (that's why 6,3,3 works).

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