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For the frequency table : 4, 8, 12, 16 | f: 5, p, 4, 3, the mean is 9. Find p.

Class 9StatisticsStatistics and Probability
  • A6
  • B10
  • C7
  • D8

Step-by-Step Solution

Σfx = 4· and Σ. Setting gives , so . Check: Σfx = 180, Σ, mean = 9.
Answer: D) 8

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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