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For the data 0–10: 5, 10–20: 25, 20–30: 16, 30–40: 18, 40–50: 8, the modal class and the median class are ____.

Class 10StatisticsStatistics and Probability
  • Aboth 10–20
  • B10–20 and 20–30 respectively
  • C20–30 and 10–20 respectively
  • D10–20 and 30–40 respectively

Step-by-Step Solution

n = 72. The highest frequency is 25, so the modal class is 10–20. The cumulative frequencies are 5, 30, 46, 64, 72 and n/2 = 36; the first cf ≥ 36 is 46, so the median class is 20–30. The two classes are located by different rules and need not agree.
Answer: B) 10–20 and 20–30 respectively

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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