To find the mean score for Group B, we can use the information given:
- The total number of students is 30.
- Therefore, each group (Group A and Group B) has 15 students (30 / 2 = 15).
- The mean score for Group A is 91%.
- 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.