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The scores for an online exam for a class of 30 students were randomly split into two groups of equal size, Group A and Group B...Question
The scores for an online exam for a class of 30 students were randomly split into two groups of equal size, Group A and Group B. Group A had a mean score of 91%. It was then found that the entire class had a mean score of 88%. What can be said about the mean score for Group B?
A. The mean score for Group B will be equal to the mean score for the entire class.
B. The mean score for Group B will be lower than the mean score for the entire class.
C. The mean score for Group B will be the same as the mean score for Group A.
D. The mean score for Group B will be higher than the mean score for the entire class.
A. The mean score for Group B will be equal to the mean score for the entire class.
B. The mean score for Group B will be lower than the mean score for the entire class.
C. The mean score for Group B will be the same as the mean score for Group A.
D. The mean score for Group B will be higher than the mean score for the entire class.
Answers
GPT-4o mini
To determine the mean score for Group B based on the given information, we can use the following approach:
1. **Calculate the total score for the entire class**:
Since the mean score for the entire class of 30 students is 88%, the total score for all students can be calculated as:
\[
\text{Total score} = \text{Mean score} \times \text{Number of students} = 88\% \times 30 = 2640
\]
2. **Calculate the total score for Group A**:
Group A has a mean score of 91%, and since it consists of 15 students (half of 30), the total score for Group A is:
\[
\text{Total score for Group A} = 91\% \times 15 = 1365
\]
3. **Calculate the total score for Group B**:
The total score for Group B can be found by subtracting the total score of Group A from the total score of the entire class:
\[
\text{Total score for Group B} = \text{Total score of entire class} - \text{Total score for Group A} = 2640 - 1365 = 1275
\]
4. **Calculate the mean score for Group B**:
The mean score for Group B is calculated by dividing the total score for Group B by the number of students in Group B (which is 15):
\[
\text{Mean score for Group B} = \frac{\text{Total score for Group B}}{15} = \frac{1275}{15} = 85\%
\]
Now we can interpret the results:
- **Mean score for Group A**: 91%
- **Mean score for Group B**: 85%
- **Mean score for the entire class**: 88%
From the calculations, we can see that the mean score for Group B (85%) is indeed lower than the mean score for the entire class (88%).
Thus, the correct answer is:
**B. The mean score for Group B will be lower than the mean score for the entire class.**
1. **Calculate the total score for the entire class**:
Since the mean score for the entire class of 30 students is 88%, the total score for all students can be calculated as:
\[
\text{Total score} = \text{Mean score} \times \text{Number of students} = 88\% \times 30 = 2640
\]
2. **Calculate the total score for Group A**:
Group A has a mean score of 91%, and since it consists of 15 students (half of 30), the total score for Group A is:
\[
\text{Total score for Group A} = 91\% \times 15 = 1365
\]
3. **Calculate the total score for Group B**:
The total score for Group B can be found by subtracting the total score of Group A from the total score of the entire class:
\[
\text{Total score for Group B} = \text{Total score of entire class} - \text{Total score for Group A} = 2640 - 1365 = 1275
\]
4. **Calculate the mean score for Group B**:
The mean score for Group B is calculated by dividing the total score for Group B by the number of students in Group B (which is 15):
\[
\text{Mean score for Group B} = \frac{\text{Total score for Group B}}{15} = \frac{1275}{15} = 85\%
\]
Now we can interpret the results:
- **Mean score for Group A**: 91%
- **Mean score for Group B**: 85%
- **Mean score for the entire class**: 88%
From the calculations, we can see that the mean score for Group B (85%) is indeed lower than the mean score for the entire class (88%).
Thus, the correct answer is:
**B. The mean score for Group B will be lower than the mean score for the entire class.**