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Use the assumed mean method with a = 40. The table gives the ages of 30 people. Class 15–25: 6, 25–35: 11, 35–45: 7, 45–55: 4, 55–65: 2. The mean is ____.

Class 10StatisticsStatistics and Probability
  • A45
  • B40
  • C35
  • D32

Step-by-Step Solution

Class marks 20, 30, 40, 50, 60 give d = −20, −10, 0, 10, 20. Σfd = −120 − 110 + 0 + 40 + 40 = −150 and Σf = 30. Mean = a + Σfd/Σf = 40 + (−150/30) = 40 − 5 = 35. (40 means forgetting the correction term; 45 comes from dropping the minus sign.)
Answer: C) 35

Key idea: Mode for grouped data

**Modal class**: class with HIGHEST frequency.

**Mode formula**:
**Mode = ₁ − ₀) / ₁ − ₀ − ₂)**

Where:
- = lower limit of modal class
- = class width
- ₁ = frequency of modal class
- ₀ = frequency of class BEFORE modal class
- ₂ = frequency of class AFTER modal class

**Example**: Modal class 30–40 with ₁ = 12, ₀ = 5, ₂ = 8. .
Mode = ≈ 36.36.

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