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Answer :
To determine whether the mean height of the other five boys is greater than the mean height of the six girls, let's go through the problem step-by-step.
### Step 1: Calculate the total height of all the girls
We know there are 6 girls, and their mean height is 59 inches. To find the total height of the girls, we multiply the mean height by the number of girls:
[tex]\[
\text{Total height of girls} = \text{Number of girls} \times \text{Mean height of girls} = 6 \times 59 = 354 \text{ inches}
\][/tex]
### Step 2: Calculate the total height of all the boys
There are 6 boys, and the mean height of the boys is 60 inches. So, the total height of the boys can be calculated as:
[tex]\[
\text{Total height of boys} = \text{Number of boys} \times \text{Mean height of boys} = 6 \times 60 = 360 \text{ inches}
\][/tex]
### Step 3: Subtract the height of the tall boy
One of the boys is exceptionally tall at 72 inches. To find the total height of the other five boys, we subtract the height of this tall boy from the total height of all the boys:
[tex]\[
\text{Total height of other five boys} = \text{Total height of boys} - \text{Height of tall boy} = 360 - 72 = 288 \text{ inches}
\][/tex]
### Step 4: Calculate the mean height of the other five boys
To find the mean height of these five boys, we divide the total height of the other five boys by the number of boys left, which is 5:
[tex]\[
\text{Mean height of other five boys} = \frac{\text{Total height of other five boys}}{\text{Number of other boys}} = \frac{288}{5} = 57.6 \text{ inches}
\][/tex]
### Step 5: Compare the mean height of the other five boys with the mean height of the girls
The mean height of the other five boys is 57.6 inches, whereas the mean height of the girls is 59 inches. Since [tex]\( 57.6 < 59 \)[/tex], the mean height of the other five boys is not greater than the mean height of the six girls.
### Conclusion
The mean height of the other five boys is 57.6 inches, which is less than the mean height of the six girls, which is 59 inches. Therefore, the mean height of the other five boys is not greater than the mean height of the six girls.
### Step 1: Calculate the total height of all the girls
We know there are 6 girls, and their mean height is 59 inches. To find the total height of the girls, we multiply the mean height by the number of girls:
[tex]\[
\text{Total height of girls} = \text{Number of girls} \times \text{Mean height of girls} = 6 \times 59 = 354 \text{ inches}
\][/tex]
### Step 2: Calculate the total height of all the boys
There are 6 boys, and the mean height of the boys is 60 inches. So, the total height of the boys can be calculated as:
[tex]\[
\text{Total height of boys} = \text{Number of boys} \times \text{Mean height of boys} = 6 \times 60 = 360 \text{ inches}
\][/tex]
### Step 3: Subtract the height of the tall boy
One of the boys is exceptionally tall at 72 inches. To find the total height of the other five boys, we subtract the height of this tall boy from the total height of all the boys:
[tex]\[
\text{Total height of other five boys} = \text{Total height of boys} - \text{Height of tall boy} = 360 - 72 = 288 \text{ inches}
\][/tex]
### Step 4: Calculate the mean height of the other five boys
To find the mean height of these five boys, we divide the total height of the other five boys by the number of boys left, which is 5:
[tex]\[
\text{Mean height of other five boys} = \frac{\text{Total height of other five boys}}{\text{Number of other boys}} = \frac{288}{5} = 57.6 \text{ inches}
\][/tex]
### Step 5: Compare the mean height of the other five boys with the mean height of the girls
The mean height of the other five boys is 57.6 inches, whereas the mean height of the girls is 59 inches. Since [tex]\( 57.6 < 59 \)[/tex], the mean height of the other five boys is not greater than the mean height of the six girls.
### Conclusion
The mean height of the other five boys is 57.6 inches, which is less than the mean height of the six girls, which is 59 inches. Therefore, the mean height of the other five boys is not greater than the mean height of the six girls.
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