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In a school survey the mean height of 20 boys is 150 cm and the mean height of 30 girls is 145 cm. Find the mean height of all 50 students.

Class 9StatisticsStatistics and Probability
  • A147.5 cm
  • B147 cm
  • C145 cm
  • D149 cm

Step-by-Step Solution

Total height = cm. Total students = 50, so the mean = cm. Simply averaging 150 and 145 to get 147.5 is wrong, because the two groups are not the same size.
Answer: B) 147 cm

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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