The problem asks for the new average score of all students after adding the scores of four more students to an already existing group of 36 students.

Here's how to approach it:

• Initial information:
  • The average score of the original 36 students is 86.
  • Four additional students have an average score of 80.
  • We need to find the new average score for all 40 students (36 original + 4 additional).

Step-by-Step Calculation:

1. Total score of the first group (36 students): $\text{Total score of 36 students} = 36 \times 86 = 3096$

2. Total score of the second group (4 students): $\text{Total score of 4 students} = 4 \times 80 = 320$

3. Total score of all 40 students: $\text{Total score of all 40 students} = 3096 + 320 = 3416$

4. New average score for 40 students: $\text{New average} = \frac{3416}{40} = 85.4$

Thus, the new average score is 85.4, which corresponds to option B.

Let me know if you'd like further clarification, or if you have any more questions!

Related Questions:

1. What is the effect of adding lower average scores to a group with a higher average?
2. How would the calculation change if the four additional students had an average of 90 instead of 80?
3. How do you calculate the total score from the average and the number of students?
4. How does the total number of students affect the average score in such problems?
5. What is the importance of weighted averages in combining different groups?

Tip:

When dealing with averages of groups, always calculate the total for each group separately before combining them to get the overall average.