Multiple choice

Directions: Answer the questions independently of each other. 5 Scores in a classroom are broken into 5 different ranges, 51-60, 61-70, 71-80, 81-90 and 91-100. The number of students who have scored in each range is given below. 51 to 60 - 5 students, 61 to 70 - 10 students, 71 to 80 - 10 students, 81 to 90 - 4 students, 91 to 100 - 3 students. Furthermore, we know that the number of students who scored 80 or more is just one more than those who scored below 76. What is the maximum possible average overall of this class?

  1. 76.84

  2. 77.26

  3. 78.46

  4. 78.54
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let N1=5, N2=10, N3=10, N4=4, N5=3. Total students = 32. Let S be the number of students scoring 80 or more (N4+N5 = 7). Let X be the number of students scoring below 76. We are told S = X + 1, so X = 6. To maximize the average, we assume students in each range score at the upper bound. For 71-80, we have 10 students; 4 must be >= 76 to satisfy X=6 (since 5+10+1=16 students are below 71, but we need 6 below 76, so 6-5=1 student in the 71-75 range). Calculating the weighted sum with max values gives the result.

Keep practicing — related questions