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The mean of 9 observations is 16. The mean of the first four is 14 and the mean of the last four is 18. Find the fifth observation.

Class 9StatisticsStatistics and Probability
  • A14
  • B18
  • C32
  • D16

Step-by-Step Solution

Total of all nine = . The first four add to and the last four add to , together 128. The fifth observation = 144 − 128 = 16.
Answer: D) 16

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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