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The mean of 30 observations is 25. It was later found that one observation 35 was wrongly read as 25. Find the correct mean.

Class 9StatisticsStatistics and Probability
  • A22.33
  • B28.33
  • C25.33
  • D50.66

Step-by-Step Solution

Wrong sum = . Correct sum = 750 − 25 + 35 = 760. Correct mean = ≈ 25.33.
Answer: C) 25.33

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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