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Difficulty: MediumDescriptive Statistics and Data Representations

At a university, three sections of an introductory chemistry course took the same midterm examination. Section 1 has 1515 students with a mean score of 8080 points, Section 2 has 2525 students with a mean score of 8888 points, and Section 3 has 1010 students with a mean score of 7474 points. What is the overall mean score for all 5050 students combined?

  1. A
    78.678.6
  2. B
    80.780.7
  3. 82.882.8Answer
  4. D
    84.084.0
  5. E
    1,380.01,380.0

Answer

The overall mean score for all 5050 students combined is 82.882.8.
To find the combined mean score for all 5050 students, calculate the total points earned across all three sections and divide by the total number of students. Section 1 contributes 15×80=1,20015 \times 80 = 1,200 points, Section 2 contributes 25×88=2,20025 \times 88 = 2,200 points, and Section 3 contributes 10×74=74010 \times 74 = 740 points. Summing these yields 4,1404,140 total points. Dividing 4,1404,140 by the total student count of 5050 gives an overall mean of 82.882.8.

Step-by-Step Solution

1
Calculate the total number of points earned by each section.
Section 1: 15×80=1,20015 \times 80 = 1,200 points. Section 2: 25×88=2,20025 \times 88 = 2,200 points. Section 3: 10×74=74010 \times 74 = 740 points.
The total points in a group equals the number of items multiplied by the mean of that group.
2
Sum the total points from all three sections to find the combined total points.
1,200+2,200+740=4,1401,200 + 2,200 + 740 = 4,140 total points.
To find the overall mean, we need the total score across all students.
3
Divide the total points by the total number of students.
4,14050=82.8\frac{4,140}{50} = 82.8.
The weighted mean is the total accumulated score divided by the total sample size (15+25+10=5015 + 25 + 10 = 50).

Key Concept

Weighted Mean
Estimated Time:1m 15s
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Topics

Descriptive Statistics and Data Representations

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