- A32
- B13
- C40
- D45
Step-by-Step Solution
Class marks 10, 30, 50, 70, 90 give Σfx = and Σ. From , so and . Total = 32 + 13 = 45. (13 is the missing frequency, not the total; 32 is the total of the known frequencies only.)
Answer: D) 45
The mean of the following data is 46. Class 0–20: 7, 20–40: f, 40–60: 12, 60–80: 8, 80–100: 5. How many observations are there in all?
Class 10StatisticsStatistics and Probability
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.
**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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