Find Number Groups with Average 7: Mean Value Selection

Q: Why does zero count as a number in the average?

Zero is a real number that affects the calculation! Even though it doesn't change the sum, it increases the count of numbers, which changes the average. Never ignore zeros when counting.

Q: What if I see the same number repeated like the two 6's?

Count every instance separately! If you see 6, 19, 6, 4, 0 - that's five numbers total, not four. Repeated values are still individual data points.

Q: How can I double-check my arithmetic quickly?

After finding the average, multiply it by the count of numbers. You should get back to your original sum: $ 7 \times 5 = 35 $ ✓

Q: Which group should I calculate first?

Start with whichever group looks easiest to add - maybe the one with smaller numbers or fewer terms. There's no required order, just be systematic!

Q: What if my calculated average isn't a whole number?

That's completely normal! Averages can be decimals or fractions. In this problem, we needed exactly 7, but many real-world averages are decimal values.

Mean Calculation with Multi-Element Sets

Choose the group of numbers of which 7 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 7

00:03 To calculate the average, we'll sum and divide by the number of occurrences

00:08 We'll use the formula for calculating average to find the average

00:22 This is the average, now let's move to the next group

00:29 We'll use the formula for calculating average to find the average

00:46 This is the average, now let's move to the next group

00:52 We'll use the formula for calculating average to find the average

01:14 This is the average, now let's move to the next group

01:17 We'll use the formula for calculating average to find the average

01:23 This is the average

01:28 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

Choose the group of numbers of which 7 is the average.

Step-by-step solution

To find the correct group of numbers with an average of 7, follow these steps:

Let's calculate the average for each group:

Group 1: $22, 6, 8, 4$
Calculate the sum: $22 + 6 + 8 + 4 = 40$
There are 4 numbers, so the average: $\frac{40}{4} = 10$
Group 2: $6, 19, 6, 4, 0$
Calculate the sum: $6 + 19 + 6 + 4 + 0 = 35$
There are 5 numbers, so the average: $\frac{35}{5} = 7$
Group 3: $7, 0, 7, 7$
Calculate the sum: $7 + 0 + 7 + 7 = 21$
There are 4 numbers, so the average: $\frac{21}{4} = 5.25$
Group 4: $8, 4, 3$
Calculate the sum: $8 + 4 + 3 = 15$
There are 3 numbers, so the average: $\frac{15}{3} = 5$

From these calculations, Group 2 with $6, 19, 6, 4, 0$ has an average of 7.

Therefore, the correct group of numbers is $6, 19, 6, 4, 0$ .

Final Answer

$6,19,6,4,0$

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum of all numbers divided by count
Method: Add all values first: 6 + 19 + 6 + 4 + 0 = 35
Verify: Check that $\frac{35}{5} = 7$ matches the target average ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count all numbers in the set
Don't forget to include zero or repeated numbers in your count = wrong denominator! Students often skip counting 0 or think repeated numbers like two 6's count as one. Always count every single number in the list, including zeros and repeats.

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 does zero count as a number in the average?

Zero is a real number that affects the calculation! Even though it doesn't change the sum, it increases the count of numbers, which changes the average. Never ignore zeros when counting.

What if I see the same number repeated like the two 6's?

Count every instance separately! If you see 6, 19, 6, 4, 0 - that's five numbers total, not four. Repeated values are still individual data points.

How can I double-check my arithmetic quickly?

After finding the average, multiply it by the count of numbers. You should get back to your original sum: $7 \times 5 = 35$ ✓

Which group should I calculate first?

Start with whichever group looks easiest to add - maybe the one with smaller numbers or fewer terms. There's no required order, just be systematic!

What if my calculated average isn't a whole number?

That's completely normal! Averages can be decimals or fractions. In this problem, we needed exactly 7, but many real-world averages are decimal values.

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