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A frequency table has the classes 0–10, 10–20, 20–30 and 30–40 with frequencies 7, ?, 12 and 6. The total frequency is 40. Find the missing frequency.

Class 9StatisticsStatistics and Probability
  • A25
  • B13
  • C15
  • D16

Step-by-Step Solution

The known frequencies add to 7 + 12 + 6 = 25. Since all frequencies must total 40, the missing frequency = 40 − 25 = 15.
Answer: C) 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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