Question

The arithmetic means of score of a group of students in a test was 52 The brightest 20% secure 80 as mean and the dullest 25% secure mean of 31 . The mean score of remaining 55%?

• A. 51.4
• B. 54.6
• C. 52
• D. 55

Answer 1

Answer:

A. 51.4

• Total Sum of Scores: If we assume the total number of students is 100 (a common simplification in percentage-based problems), the total sum of scores for the entire group would be Total Students × Overall Mean. So, 100 × 52 = 5200.

• Sum for the Brightest 20%: This group constitutes 20% of the students, which is 20 students. Their mean score is 80. Therefore, their total sum of scores is 20 × 80 = 1600.

• Sum for the Dullest 25%: This group constitutes 25% of the students, which is 25 students. Their mean score is 31. Therefore, their total sum of scores is 25 × 31 = 775.

• Remaining Students: The percentage of remaining students is 100% - 20% - 25% = 55%. This means there are 55 students in this group.

• Sum for Remaining 55%: Let the mean score of this remaining group be X. The total sum of scores for this group will be 55 × X.

• Applying the Principle of Conservation of Sum: The sum of scores of all individual groups must equal the total sum of scores for the entire group.
  Sum of brightest + Sum of dullest + Sum of remaining = Total Sum
  1600 + 775 + (55 × X) = 5200

• Solving for X:
  2375 + 55X = 5200
  55X = 5200 - 2375
  55X = 2825
  X = 2825 / 55

• Calculating the Mean: X ≈ 51.36, which is typically rounded to 51.4.