The mean of marks secured by 25 students of section A of a class is 47, for 51 students of section B is 51, and for 30 students of section C is 53. Find the mean of marks of the students of all three sections of class X.

1. A

   50

2. B

   50.6

3. C

   52.5

4. D

   54.5

Appeared in: BSF Staff Nurse - 2015

Explanation

• The problem requires calculating a weighted average because the groups (class sections) have different sizes (number of students).
• First, find the total sum of marks for all students by multiplying the number of students in each section by their respective mean score and then adding these products together: (25 × 47) + (51 × 51) + (30 × 53) = 1175 + 2601 + 1590 = 5366.
• Next, find the total number of students by summing the students in all sections: 25 + 51 + 30 = 106.
• Finally, divide the total sum of marks by the total number of students to get the combined mean: 5366 ÷ 106 ≈ 50.6.

Why Other Options Were Wrong

• Option A: This value is incorrect. It may result from a calculation error or rounding incorrectly.
• Option C: This value is too high and does not reflect the weighted contribution of each section's mean score.
• Option D: This value is significantly higher than the calculated weighted mean.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the weighted mean of multiple groups as background academic context rather than a clinical decision trigger.
• The concept of weighted averages is used in healthcare research to combine results from different studies or patient populations in a meta-analysis.
• In hospital administration, it can be used to calculate average patient satisfaction scores across different wards with varying numbers of patients.
• What if? If all three sections had the same number of students (e.g., 30 each), you could simply calculate the simple average of the means: (47 + 51 + 53) / 3 = 50.33. However, since the group sizes are different, a weighted average is necessary.

How to Approach the Question

• Identify that the question asks for a combined mean from groups of different sizes. This indicates the need for a weighted average, not a simple average.
• List the data for each group: size (n) and mean (x).
• For each group, calculate the total value by multiplying its size by its mean (n × x).
• Sum the total values from all groups to get the overall total.
• Sum the sizes of all groups to get the overall size.
• Divide the overall total value by the overall total size to find the weighted mean.

Concept Tested & Keywords

• Concept Tested: Calculating the weighted mean of multiple groups.
• Stem keywords: mean of marks, 25 students, section A, 51 students, section B, 30 students, section C
• Lead-in keywords: Find the mean

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QgLMHaladXYTM5usQFwGet

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