Case Study 3:

The 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.

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Question

Case Study 3:

The 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.

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The table below shows sub-divisions wise seasonal (monsoon) rainfall (in mm) in 2023.

| Rainfall (mm) | No. of Sub-divisions |
|---------------|---------------------|
| $200 - 400$ | $3$ |
| $400 - 600$ | $4$ |
| $600 - 800$ | $7$ |
| $800 - 1000$ | $4$ |
| $1000 - 1200$ | $3$ |
| $1200 - 1400$ | $3$ |

Based on the information given above, answer the following questions:
(i) Write the modal class.
(ii) (a) Find the median of the given data.
**OR**
(b) Find the mean rainfall in the season.
(iii) If a sub-division having at least 800 mm rainfall during monsoon season is considered a good rainfall sub-division, then how many sub-divisions had good rainfall?

Accepted Answer

Step 1: (i) Modal Class $= 600 - 800$
Step 2: (ii)(a)

| Rainfall (mm) | No. of Sub-divisions ($f$) | $cf$ |
|---------------|---------------------------|------|
| $200 - 400$ | $3$ | $3$ |
| $400 - 600$ | $4$ | $7$ |
| $600 - 800$ | $7$ | $14$ |
| $800 - 1000$ | $4$ | $18$ |
| $1000 - 1200$ | $3$ | $21$ |
| $1200 - 1400$ | $3$ | $24$ |

$N = 24$, Median Class $= 600 - 800$
Median $= 600 + \frac{12 - 7}{7} 	imes 200 = \frac{5200}{7}$ or $742.8$ mm (approx.)
Step 3: **OR**
(ii)(b)

| Rainfall (mm) | No. of Sub-divisions ($f_i$) | $x_i$ | $f_i x_i$ |
|---------------|------------------------------|--------|------------|
| $200 - 400$ | $3$ | $300$ | $900$ |
| $400 - 600$ | $4$ | $500$ | $2000$ |
| $600 - 800$ | $7$ | $700$ | $4900$ |
| $800 - 1000$ | $4$ | $900$ | $3600$ |
| $1000 - 1200$ | $3$ | $1100$ | $3300$ |
| $1200 - 1400$ | $3$ | $1300$ | $3900$ |
| | $\sum f_i = 24$ | | $\sum f_i x_i = 18600$ |

Mean $= \frac{18600}{24} = 775$
$	herefore$ Mean rainfall $= 775$ mm
Step 4: (iii) Required number of sub-divisions $= 4 + 3 + 3 = 10$

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