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The lowest temperatures on six winter days were −4 °C, 2 °C, −7 °C, 5 °C, 0 °C and 3 °C. Find the range.

Class 9StatisticsStatistics and Probability
  • A−2 °C
  • B9 °C
  • C7 °C
  • D12 °C

Step-by-Step Solution

Largest = 5 °C and smallest = −7 °C. Range = 5 − (−7) = 5 + 7 = 12 °C. Writing 5 − 7 = −2 forgets that subtracting a negative number adds it.
Answer: D) 12 °C

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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