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Difficulty: MediumDescriptive Statistics and Data Representations

A university professor teaches two sections of Introductory Statistics. Section 1 contains 3030 students and had a mean score of 8282 on the midterm exam. Section 2 contains 2020 students and had a mean score of 9292 on the same exam. What is the overall mean midterm exam score for all 5050 students combined?

  1. A
    85
  2. 86Answer
  3. C
    87
  4. D
    88
  5. E
    90

Answer

The overall mean score for all 50 students combined is 86.
To find the combined mean score for all students, calculate the total points earned by multiplying each section's mean by its number of students, summing those products, and dividing by the total number of students: (30×82)+(20×92)30+20=2,460+1,84050=4,30050=86\frac{(30 \times 82) + (20 \times 92)}{30 + 20} = \frac{2,460 + 1,840}{50} = \frac{4,300}{50} = 86.

Step-by-Step Solution

1
Calculate total points scored by Section 1
30×82=2,46030 \times 82 = 2,460 points
Multiplying the number of students by their mean score yields the sum of their scores.
2
Calculate total points scored by Section 2
20×92=1,84020 \times 92 = 1,840 points
Multiplying the number of students in Section 2 by their mean score yields their point total.
3
Calculate total points scored across both sections
2,460+1,840=4,3002,460 + 1,840 = 4,300 points
Adding the total points from both sections gives the total combined points.
4
Divide total combined points by total combined students
4,30050=86\frac{4,300}{50} = 86
Dividing the sum of all scores by the total number of students gives the combined mean.

Key Concept

Weighted Mean of Combined Sets
Estimated Time:1m 30s
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Topics

Descriptive Statistics and Data Representations

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