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Measurements are grouped as 10.1–10.5, 10.6–11.0, 11.1–11.5. After the classes are made continuous, the upper boundary of the first class is ____.

Class 10StatisticsStatistics and Probability
  • A10.5
  • B10.6
  • C10.45
  • D10.55

Step-by-Step Solution

The gap is 10.6 − 10.5 = 0.1, so the adjustment is 0.05 — not 0.5. The first class becomes 10.05–10.55, so its upper boundary is 10.55, which is also the lower boundary of the next class.
Answer: D) 10.55

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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