India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018 :
Based on the above information, answer the following questions.
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding stimulus
Model Answer
(I) Modal Class:
The class with the highest frequency is 600–800 (frequency = 7).
∴ Modal class = 600–800
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(II) Median:
| Class | Frequency | Cumulative Frequency |
|-------|-----------|----------------------|
| 200–400 | 2 | 2 |
| 400–600 | 4 | 6 |
| 600–800 | 7 | 13 |
| 800–1000 | 4 | 17 |
| 1000–1200 | 2 | 19 |
| 1200–1400 | 3 | 22 |
| 1400–1600 | 1 | 23 |
| 1600–1800 | 1 | 24 |
Total $n = 24$, so $\dfrac{n}{2} = 12$
Median class = 600–800 (cf just before = 6, f = 7, l = 600, h = 200)
$$\text{Median} = l + \frac{\frac{n}{2} - cf}{f} \times h = 600 + \frac{12 - 6}{7} \times 200 = 600 + \frac{1200}{7} \approx \textbf{771.43 mm}$$
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(III) Good Rainfall Sub-divisions:
Sub-divisions with rainfall ≥ 1000 mm: 2 + 3 + 1 + 1 = 7 sub-divisions
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Explanation
- (I) Modal class is simply the class with the highest frequency — no calculation needed.
- (II) Always build the cf table first; identify median class where cf first exceeds n/2. Apply the formula correctly showing all steps.
- (III) Add frequencies of all classes from 1000 mm onwards (1000–1200, 1200–1400, 1400–1600, 1600–1800). Examiners look for correct addition.