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Mathematics · 2025 · 4 marks
CBSE 2025 · Region 3 · Set 1 · Q38
The India Meteorological Department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to…
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.
The table below shows sub-divisions wise seasonal (monsoon) rainfall (in mm) in 2023.
Based on the information given above, answer the following questions :
| Rainfall (mm) | No. of Sub-divisions |
| $\displaystyle 200$-$\displaystyle 400$ | $\displaystyle 3$ |
| $\displaystyle 400$-$\displaystyle 600$ | $\displaystyle 4$ |
| $\displaystyle 600$-$\displaystyle 800$ | $\displaystyle 7$ |
| $\displaystyle 800$-$\displaystyle 1000$ | $\displaystyle 4$ |
| $\displaystyle 1000$-$\displaystyle 1200$ | $\displaystyle 3$ |
| $\displaystyle 1200$-$\displaystyle 1400$ | $\displaystyle 3$ |
(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 $\displaystyle 800$ mm rainfall during monsoon season is considered a good rainfall sub-division, then how many sub-divisions had good rainfall ?
Marking-scheme solution
(i)
Modal Class \(\displaystyle =600-800\)
(ii)
| Rainfall (mm) | No. of Sub-divisions \(\displaystyle \left(\boldsymbol{f}_{\boldsymbol{i}}\right)\) | \(\displaystyle \boldsymbol{c} \boldsymbol{f}\) |
| $\displaystyle 200$-$\displaystyle 400$ | $\displaystyle 3$ | $\displaystyle 3$ |
| $\displaystyle 400$-$\displaystyle 600$ | $\displaystyle 4$ | $\displaystyle 7$ |
| $\displaystyle 600$-$\displaystyle 800$ | $\displaystyle 7$ | $\displaystyle 14$ |
| $\displaystyle 800$-$\displaystyle 1000$ | $\displaystyle 4$ | $\displaystyle 18$ |
| $\displaystyle 1000$-$\displaystyle 1200$ | $\displaystyle 3$ | $\displaystyle 21$ |
| $\displaystyle 1200$-$\displaystyle 1400$ | $\displaystyle 3$ | $\displaystyle 24$ |
\[N=24
\]
Median Class \(\displaystyle =600-800\)
\[\text { Median }=600+\frac{12-7}{7} \times 200
\]
\[=\frac{5200}{7} \text { or } 742.8 \mathrm{~mm} \text { (approx.) }
\]
| Rainfall (mm) | No. of Sub-divisions \(\displaystyle \left(\boldsymbol{f}_{\boldsymbol{i}}\right)\) | \(\displaystyle \boldsymbol{x}_{\boldsymbol{i}}\) | \(\displaystyle \boldsymbol{f}_{\boldsymbol{i}} \boldsymbol{x}_{\boldsymbol{i}}\) |
| $\displaystyle 200$-$\displaystyle 400$ | $\displaystyle 3$ | $\displaystyle 300$ | $\displaystyle 900$ |
| $\displaystyle 400$-$\displaystyle 600$ | $\displaystyle 4$ | $\displaystyle 500$ | $\displaystyle 2000$ |
| $\displaystyle 600$-$\displaystyle 800$ | $\displaystyle 7$ | $\displaystyle 700$ | $\displaystyle 4900$ |
| $\displaystyle 800$-$\displaystyle 1000$ | $\displaystyle 4$ | $\displaystyle 900$ | $\displaystyle 3600$ |
| $\displaystyle 1000$-$\displaystyle 1200$ | $\displaystyle 3$ | $\displaystyle 1100$ | $\displaystyle 3300$ |
| $\displaystyle 1200$-$\displaystyle 1400$ | $\displaystyle 3$ | $\displaystyle 1300$ | $\displaystyle 3900$ |
| \(\displaystyle \sum f_{i}=24\) | \(\displaystyle \sum f_{i} x_{i}=18600\) |
\[\text { Mean }=\frac{18600}{24}=775
\]
\(\displaystyle \therefore\) Mean rainfall \(\displaystyle =775 \mathrm{~mm}\)
(iii)
Required number of sub-divisions \(\displaystyle =4+3+3=10\)
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