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?(1 point) Responses The mean score for Group B will be equal to the mean score for the entire class. The mean score for Group B will be equal to the mean score for the entire class. The mean score for Group B will be lower than the mean score for the entire class. The mean score for Group B will be lower than the mean score for the entire class. The mean score for Group B will be the same as the mean score for Group A. The mean score for Group B will be the same as the mean score for Group A. The mean score for Group B will be higher than the mean score for the entire class.
Answers
GPT-4o mini
To find the mean score for Group B, we can use the information given:
1. The total number of students is 30.
2. Therefore, each group (Group A and Group B) has 15 students (30 / 2 = 15).
3. The mean score for Group A is 91%.
4. The mean score for the entire class of 30 students is 88%.
To find the mean score for Group B, we can set up an equation based on the overall mean:
Let \( \text{Mean score of Group B} = x \).
The contribution to the overall mean from Group A and Group B can be represented as follows:
\[
\frac{(\text{Mean Group A} \times \text{Number of students in Group A}) + (\text{Mean Group B} \times \text{Number of students in Group B})}{\text{Total number of students}} = \text{Overall Mean}
\]
Substituting the values:
\[
\frac{(91 \times 15) + (x \times 15)}{30} = 88
\]
Multiplying both sides by 30 to eliminate the denominator:
\[
(91 \times 15) + (x \times 15) = 88 \times 30
\]
Calculating the values:
\[
1365 + 15x = 2640
\]
Now, solve for \( x \):
\[
15x = 2640 - 1365
\]
\[
15x = 1275
\]
\[
x = \frac{1275}{15} = 85
\]
Thus, the mean score for Group B is 85%.
Since the mean score for Group B (85%) is lower than the overall class mean (88%), we can conclude that:
**The mean score for Group B will be lower than the mean score for the entire class.**
1. The total number of students is 30.
2. Therefore, each group (Group A and Group B) has 15 students (30 / 2 = 15).
3. The mean score for Group A is 91%.
4. The mean score for the entire class of 30 students is 88%.
To find the mean score for Group B, we can set up an equation based on the overall mean:
Let \( \text{Mean score of Group B} = x \).
The contribution to the overall mean from Group A and Group B can be represented as follows:
\[
\frac{(\text{Mean Group A} \times \text{Number of students in Group A}) + (\text{Mean Group B} \times \text{Number of students in Group B})}{\text{Total number of students}} = \text{Overall Mean}
\]
Substituting the values:
\[
\frac{(91 \times 15) + (x \times 15)}{30} = 88
\]
Multiplying both sides by 30 to eliminate the denominator:
\[
(91 \times 15) + (x \times 15) = 88 \times 30
\]
Calculating the values:
\[
1365 + 15x = 2640
\]
Now, solve for \( x \):
\[
15x = 2640 - 1365
\]
\[
15x = 1275
\]
\[
x = \frac{1275}{15} = 85
\]
Thus, the mean score for Group B is 85%.
Since the mean score for Group B (85%) is lower than the overall class mean (88%), we can conclude that:
**The mean score for Group B will be lower than the mean score for the entire class.**