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The bar graph shows the runs Smriti scored in six matches. Find her mean score, and the number of matches in which she scored more than her mean.

Class 9StatisticsStatistics and Probability
  • AMean 48; 2 matches
  • BMean 40; 4 matches
  • CMean 42.5; 3 matches
  • DMean 40; 3 matches

Step-by-Step Solution

Total runs , so mean . She scored more than in matches 1, 3 and 5, i.e. matches itself is not more).
Answer: D) Mean 40; 3 matches

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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