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The mean weight of a group of 10 students is 60 kg and the mean weight of a second group is 80 kg. Taken together, the mean weight of all the students is 72 kg. How many students are in the second group?

Class 9StatisticsStatistics and Probability
  • A15
  • B12
  • C20
  • D18

Step-by-Step Solution

Let the second group have students. Total weight both ways: , so , giving and .
Answer: A) 15

Key idea: Mean of ungrouped data

**Formula**: ̄ = (sum of observations) / (number of observations) = Σ.

**Example**: Marks of 5 students: 7, 8, 6, 9, 10.
Sum = 40, . Mean = 40/5 = 8.

**For a frequency distribution**:
̄ = Σᵢᵢ) / Σᵢ
Multiply each value by its frequency, sum, and divide by total frequency.

Example: marks 5, 7, 9 with frequencies 2, 3, 5.
Σ·2 + 7·3 + 9·5 = 10 + 21 + 45 = 76.
Σ. Mean = 76 / 10 = 7.6.

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