Let’s solve the problem step by step.

Problem Breakdown:

1. Mean of 20 students is 65:

   • The total score of these 20 students is: $\text{Total} = \text{Mean} \times \text{Number of students} = 65 \times 20 = 1300.$

2. Two new students are added with scores of 89 and 85:

   • The total score of the two students is: $89 + 85 = 174.$

3. New total score of all students:

   • Total score = Previous total + New scores: $1300 + 174 = 1474.$

4. New number of students:

   • Total number of students = 20 + 2 = 22.

5. New mean score:

   • New mean = New total score ÷ New number of students: $\text{New Mean} = \frac{1474}{22} = 67.$

Final Answer:

The new mean of the group is 67.
The correct choice is E.

Would you like a detailed explanation for any step?

5 Related Questions:

1. What happens to the mean if more students with lower scores are added?
2. How is the median of the scores affected in this scenario?
3. What is the range of scores if the highest and lowest are considered?
4. Can the variance of the scores be calculated with this information?
5. How does adding outliers (very high or low scores) affect the mean?

Tip:

When adding new values to a group, check if the new values are above or below the current mean to determine whether the mean will increase or decrease!