Averages for 5th Grade: Finding a group with a specific average

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: $1, 2$
  - Sum = $1 + 2 = 3$
  - Count = $2$
  - Average = $\frac{3}{2} = 1.5$
• Choice 2: $3, 3$
  - Sum = $3 + 3 = 6$
  - Count = $2$
  - Average = $\frac{6}{2} = 3$
• Choice 3: $2, 0$
  - Sum = $2 + 0 = 2$
  - Count = $2$
  - Average = $\frac{2}{2} = 1$
• Choice 4: $2, 2, 2, 2$
  - Sum = $2 + 2 + 2 + 2 = 8$
  - Count = $4$
  - Average = $\frac{8}{4} = 2$

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

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

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: $2, 2$

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

Choice 2: $6, 3, 3$

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

Choice 3: $6, 4, 5$

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

Choice 4: $4, 0, 0$

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

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

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

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

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

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

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

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

• Step 1: Identify the groups and calculate the average for each.

• Step 2: Compare the calculated averages with 5.

Now, let's apply these steps:
Step 1: - For choice (a), the group is $\{5\}$. The average is $\frac{5}{1} = 5$.
- For choice (b), the group is $\{5, 0\}$. The average is $\frac{5 + 0}{2} = \frac{5}{2} = 2.5$.
- For choice (c), the group is $\{5, 5, 5\}$. The average is $\frac{5 + 5 + 5}{3} = \frac{15}{3} = 5$.

Step 2: The calculated averages for choices (a) and (c) are 5.

Therefore, the groups of numbers for which 5 is the average are choices (a) and (c).

Hence, the correct answer is Answers (a) and (c) are correct.

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:

Now, let's calculate and analyze:

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

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

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

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

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

To solve this problem, we'll follow these steps to verify if each group of numbers has an average of 8:

• Calculate the average for each group of numbers provided in the answer choices.

Let's calculate:

• Choice 1: $10, 8, 12, 2$
  Sum = $10 + 8 + 12 + 2 = 32$
  Count = 4
  Average = $\frac{32}{4} = 8$
• Choice 2: $24, 0, 0$
  Sum = $24 + 0 + 0 = 24$
  Count = 3
  Average = $\frac{24}{3} = 8$
• Choice 3: $8, 8, 8$
  Sum = $8 + 8 + 8 = 24$
  Count = 3
  Average = $\frac{24}{3} = 8$

Therefore, all choices result in an average of 8.

This verifies that All answers are correct.

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 $6, 19, 6, 4, 0$.

To solve this problem, we'll evaluate the average (mean) of each group's numbers provided in the options and find out which one equals $5\frac{1}{2}$.

• Step 1: Calculate the mean for each group.

Let's start with the options:

Option 1: $4, 4, 5$

Sum: $4 + 4 + 5 = 13$
Number of terms: 3
Average: $\frac{13}{3} = 4.33$ (not $5\frac{1}{2}$)

Option 2: $2, 9$

Sum: $2 + 9 = 11$
Number of terms: 2
Average: $\frac{11}{2} = 5.5$ (This matches $5\frac{1}{2}$)

Option 3: $4, 5, 6, 9$

Sum: $4 + 5 + 6 + 9 = 24$
Number of terms: 4
Average: $\frac{24}{4} = 6$ (not $5\frac{1}{2}$)

Option 4: $2, 9, 1$

Sum: $2 + 9 + 1 = 12$
Number of terms: 3
Average: $\frac{12}{3} = 4$ (not $5\frac{1}{2}$)

Therefore, the correct choice is the group of numbers $2, 9$. This group has an average of $5\frac{1}{2}$.