Question

A teacher gives the same math exam to two different classes. The second class has more students than the first. The mean score for the first class is 70%, and the mean score for the second class is 90%. What can you say about the mean score for both classes combined? A) It is higher than 80%. B) It is lower than 80%. C) It is equal to 80%. D) It may be higher or lower than 80%; this cannot be determined from the information given.

Answer 1

To determine the mean score for both classes combined, we need to consider the weighted average of the mean scores for each class, where the weights are based on the number of students in each class.

Let:

- M1 = Mean score for the first class (70%)

- M2 = Mean score for the second class (90%)

- N1 = Number of students in the first class

- N2 = Number of students in the second class

Since the second class has more students than the first class, we can say that N2 > N1.

To find the weighted average, we need to consider the proportion of students in each class:

Weighted Average = ( (M1 * N1) + (M2 * N2) ) / (N1 + N2)

Now, let's consider the possible scenarios:

1. If N2 is significantly larger than N1, then the impact of the higher mean score of the second class (M2 = 90%) will have a greater influence on the combined mean.

2. If N2 is only slightly larger than N1, then the impact of the higher mean score of the second class (M2 = 90%) may be mitigated to some extent.

Without specific information about the values of N1 and N2, we cannot definitively say whether the combined mean score is higher or lower than 80%. Therefore, the correct answer is:

D) It may be higher or lower than 80%; this cannot be determined from the information given.

Explanation: