Averages for 5th Grade: Identify the greater value

To solve this problem, we need to compare the given values: $17$, $15$, $12$, $12$, and $9$, and choose the sign between the middle values $15$ and $12$.

Step-by-step analysis:

• Step 1: Consider the numbers
  We're given the sequence $17$, $15$, $?$, $12$, $12$, and $9$. We're tasked to find the correct symbol to place in the sequence comparing $15$ with $12$.
• Step 2: Compare the values
  $15$ and $12$ are part of the sequence list. Clearly, $15$ is greater than $12$.
• Step 3: Selection of the sign
  Since the number $15$ is greater than $12$, the inequality that represents this correctly is “$>$” (greater than).

Therefore, the correct inequality to place in the sequence is $>$.

To solve this problem, we'll calculate the average of each group and compare them.

• Step 1: Calculate the average of the first group $4, 4, 4, 4$:
  $\text{Sum of Group A} = 4 + 4 + 4 + 4 = 16$
  $\text{Number of elements in Group A} = 4$
  $\text{Average of Group A} = \frac{16}{4} = 4$
• Step 2: Calculate the average of the second group $1, 4, 5, 7$:
  $\text{Sum of Group B} = 1 + 4 + 5 + 7 = 17$
  $\text{Number of elements in Group B} = 4$
  $\text{Average of Group B} = \frac{17}{4} = 4.25$
• Step 3: Compare the two averages:
  $\text{Average of Group A} = 4$
  $\text{Average of Group B} = 4.25$
  Since $4 < 4.25$, the correct inequality is $4 < 4.25$.

Therefore, the appropriate sign to use is $<$.

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

• Step 1: Calculate the average of the first group of numbers: $9, 3$.
• Step 2: Calculate the average of the second group of numbers: $9, 7, 2$.
• Step 3: Compare the two averages and choose the appropriate comparison sign.

Now, let's work through each step:

Step 1: Calculate the average of the first group.

Sum of first group: $9 + 3 = 12$

Number of elements: $2$

Average: $\frac{12}{2} = 6$

Step 2: Calculate the average of the second group.

Sum of second group: $9 + 7 + 2 = 18$

Number of elements: $3$

Average: $\frac{18}{3} = 6$

Step 3: Compare the two averages.

The average of the first group is $6$, and the average of the second group is also $6$.

Since both averages are equal, the appropriate comparison sign is $=$.

Therefore, the solution to the problem is $=$.

To solve this problem, we will follow these steps:

• Step 1: Calculate the average of the first group (5, 5, 5).
• Step 2: Calculate the average of the second group (20, 0, 0, 0).
• Step 3: Compare the two averages to choose the appropriate sign.

Now, let's work through each step:

Step 1: Calculate the average of Group 1.
The sum of Group 1 is $5 + 5 + 5 = 15$.
The number of terms in Group 1 is 3.
Thus, the average of Group 1 is $\frac{15}{3} = 5$.

Step 2: Calculate the average of Group 2.
The sum of Group 2 is $20 + 0 + 0 + 0 = 20$.
The number of terms in Group 2 is 4.
Thus, the average of Group 2 is $\frac{20}{4} = 5$.

Step 3: Compare the averages.
The average of Group 1 is 5, and the average of Group 2 is also 5.
Since the averages are equal, the appropriate mathematical sign is '='.

Therefore, the correct comparison is $5, 5, 5 \stackrel{=}{=} 20, 0, 0, 0$.

The appropriate sign is =.

Let's solve the problem step by step:

• Step 1: Calculate the sum of the numbers. The numbers given are $8, 11, 10,$ and $7$.

Sum = $8 + 11 + 10 + 7 = 36$.

• Step 2: Find the average using the formula $\frac{\text{Sum}}{\text{Number of elements}}$.

The number of elements is $4$.

Average = $\frac{36}{4} = 9$.

• Step 3: Compare the average with $10$.

Since $9$ is less than $10$, we have $9 < 10$.

Therefore, the correct sign to fill in the blank is $\gt$ because we are comparing $10$ (the number on the left) with $9$ (the average) and since $10$ is greater, $10\gt8,11,10,7$.

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

• Step 1: Calculate the average of the first group $(7, 8, 4, 3, 6, 5)$.
• Step 2: Calculate the average of the second group $(3, 7, 8, 5)$.
• Step 3: Compare the two averages.

Let's complete each step in detail:

Step 1: Calculate the average of the first group.

The numbers in the first group are $7, 8, 4, 3, 6, 5$. First, find the sum:

$7 + 8 + 4 + 3 + 6 + 5 = 33$.

There are 6 numbers in this group, so the average is:

$\text{Average} = \frac{33}{6} = 5.5$.

Step 2: Calculate the average of the second group.

The numbers in the second group are $3, 7, 8, 5$. First, find the sum:

$3 + 7 + 8 + 5 = 23$.

There are 4 numbers in this group, so the average is:

$\text{Average} = \frac{23}{4} = 5.75$.

Step 3: Compare the two averages.

The average of the first group is $5.5$ and the average of the second group is $5.75$.

Therefore, $5.5$ is less than $5.75$.

We choose the sign $<$ indicating that the average of the first group is less than the average of the second group.

The correct answer is $<$.

To solve this problem, we'll determine the average of both groups and compare the results:

• Step 1: Calculate the average of the first group $(12, 16)$.
  The sum of the first group is $12 + 16 = 28$.
  There are 2 numbers, so the average is $\frac{28}{2} = 14$.
• Step 2: Calculate the average of the second group $(10, 20, 25, 5, 10)$.
  The sum of the second group is $10 + 20 + 25 + 5 + 10 = 70$.
  There are 5 numbers, so the average is $\frac{70}{5} = 14$.
• Step 3: Compare the averages.
  Both groups have an average of 14; thus, the correct sign is $=$.

Since both averages are equal, the conclusion is that the groups have the same average.
Therefore, the solution to the problem is =.

To solve this problem, follow these steps:

• Step 1: Calculate the average for the first group of numbers: 30, 30, 30.
• Step 2: Calculate the average for the second group of numbers: 30, 30, 30, 30, 30, 30.
• Step 3: Compare the two averages using the appropriate sign.

Now, let's calculate each step:

Step 1: The first group is 30, 30, 30.
The sum is $30 + 30 + 30 = 90$.
The count is 3.
The average is $\frac{90}{3} = 30$.

Step 2: The second group is 30, 30, 30, 30, 30, 30.
The sum is $30 + 30 + 30 + 30 + 30 + 30 = 180$.
The count is 6.
The average is $\frac{180}{6} = 30$.

Step 3: Compare the averages:
First average = 30 and Second average = 30. Thus, they are equal.

Therefore, the appropriate mathematical sign between the two groups is $\boxed{=}$.

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

• Step 1: Calculate the average of each group.
• Step 2: Compare the averages using the appropriate sign.

Now, let's work through each step:

Step 1: The first group is $(9,0)$. To find the average:

$\text{Average of (9,0)} = \frac{9 + 0}{2} = \frac{9}{2} = 4.5$

Step 2: The second group is $(9,0,0)$. To find the average:

$\text{Average of (9,0,0)} = \frac{9 + 0 + 0}{3} = \frac{9}{3} = 3$

Now, we compare the two averages:

$4.5$ compared to $3$.

Since $4.5$ is greater than $3$, we mark the appropriate sign as $\gt$.

Therefore, the solution to the problem is $9,0 \gt 9,0,0$.

To solve this problem, let's calculate the average for each group of numbers:

• Step 1: Calculate the average of the first group $4, 5, 10, 5, 1, 5$:
  • Sum of numbers: $4 + 5 + 10 + 5 + 1 + 5 = 30$
  • Number of elements: $6$
  • Average: $\frac{30}{6} = 5$
• Step 2: Calculate the average of the second group $4, 5, 10, 5, 1$:
  • Sum of numbers: $4 + 5 + 10 + 5 + 1 = 25$
  • Number of elements: $5$
  • Average: $\frac{25}{5} = 5$

Both groups have an average of $5$, so the correct sign to place between them is =.