a. The highest grade is 97, the least grade is 53, and the difference between them is 44.
b.
i. The grades of the five highest-ranking students are 97, 96, 95, 94, 93
ii. The grades of the five lowest-ranking students are 53, 57, 59, 60, 60
iii. The grade of the 10th highest-ranking student is 88
iv. The number of students who received grades of 75 or higher is 44
v. The number of students who received grades below 85 is 65
vi. The percentage of students who received grades higher than 65 but not higher than 85 is approximately 65%.
How to find the highest grade
(a) To find the highest grade, least grade, and the difference between them, we can analyze the given list of grades.
Grades:
84 75 82 68 79 88 73 90 62 88 76 93 71 59 85 75 78 63 72 60 75 87 82 75 74 68 89 61 83 71 67 97 76 71 75 62 76 53 74 76 75 85 77 68 73 61 66 65 74 78 94 77 96 78 75 95 79 62 78 85 65 80 73 57 78 86 67 73 81 72 63 60 93 62 95 69 60 79 65 88
Highest grade: 97
Least grade: 53
Difference between highest and least grade: 97 - 53 = 44
Therefore, the highest grade is 97, the least grade is 53, and the difference between them is 44.
(b) To find the grades of the five highest-ranking students and the five lowest-ranking students, we can sort the list of grades in descending order.
Sorted grades in descending order:
97 96 95 94 93 93 90 89 88 88 87 86 85 85 85 84 83 82 82 81 80 79 79 79 78 78 78 78 78 77 77 76 76 76 76 76 76 76 75 75 75 75 75 75 74 74 74 74 73 73 73 73 72 71 71 71 70 69 68 68 68 67 67 66 65 65 65 63 63 62 62 62 61 61 60 60 60 59 57 53
(i) Grades of the five highest-ranking students: 97, 96, 95, 94, 93
(ii) Grades of the five lowest-ranking students: 53, 57, 59, 60, 60
To find the grade of the 10th highest-ranking student, we count from the top of the sorted list:
(iii) Grade of the 10th highest-ranking student: 88
To find the number of students who received grades of 75 or higher, count the grades in the sorted list that are 75 or greater:
(iv) Number of students who received grades of 75 or higher: 44
To find the number of students who received grades below 85, count the grades in the sorted list that are less than 85:
(v) Number of students who received grades below 85: 65
To find the percentage of students who received grades higher than 65 but not higher than 85, count the grades in the sorted list that fall within that range and divide by the total number of students (80):
Number of grades in the range: 52
(vi) Percentage of students who received grades higher than 65 but not higher than 85: (52/80) * 100 ≈ 65%
Therefore, the grades of the five highest-ranking students are 97, 96, 95, 94, 93, the grades of the five lowest-ranking students are 53, 57, 59, 60, 60, the grade of the 10th highest-ranking student is 88, the number of students who received grades of 75 or higher is 44, the number of students who received grades below 85 is 65, and the percentage of students who received grades higher than 65 but not higher than 85 is approximately 65%.