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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 1 · Set 1 · Q37
India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare…
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 $\displaystyle 2018$ :
Based on the above information, answer the following questions :
| Rainfall (mm) | Number of Sub-divisions |
| $\displaystyle 200$-$\displaystyle 400$ | $\displaystyle 2$ |
| $\displaystyle 400$-$\displaystyle 600$ | $\displaystyle 4$ |
| $\displaystyle 600$-$\displaystyle 800$ | $\displaystyle 7$ |
| $\displaystyle 800$-$\displaystyle 1000$ | $\displaystyle 4$ |
| $\displaystyle 1000$-$\displaystyle 1200$ | $\displaystyle 2$ |
| $\displaystyle 1200$-$\displaystyle 1400$ | $\displaystyle 3$ |
| $\displaystyle 1400$-$\displaystyle 1600$ | $\displaystyle 1$ |
| $\displaystyle 1600$-$\displaystyle 1800$ | $\displaystyle 1$ |
(I)
Write the modal class.
(II)
Find the median of the given data.
OR Find the mean rainfall in this season.
(III)
If sub-division having at least $\displaystyle 1000$ mm rainfall during monsoon season, is considered good rainfall sub-division, then how many sub- divisions had good rainfall ?
Marking-scheme solution
(i) Modal Class is $\displaystyle 600$-$\displaystyle 800$
\(\displaystyle \frac{N}{2}=12\), median class is \(\displaystyle 600-800\)
| Rainfall | \(\displaystyle \mathrm{x}_{\mathrm{i}}\) | \(\displaystyle \mathrm{f}_{\mathrm{i}}\) | cf. |
| $\displaystyle 200$-$\displaystyle 400$ | $\displaystyle 300$ | $\displaystyle 2$ | $\displaystyle 2$ |
| $\displaystyle 400$-$\displaystyle 600$ | $\displaystyle 500$ | $\displaystyle 4$ | $\displaystyle 6$ |
| $\displaystyle 600$-$\displaystyle 800$ | $\displaystyle 700$ | $\displaystyle 7$ | $\displaystyle 13$ |
| $\displaystyle 800$-$\displaystyle 1000$ | $\displaystyle 900$ | $\displaystyle 4$ | $\displaystyle 17$ |
| $\displaystyle 1000$-$\displaystyle 1200$ | $\displaystyle 1100$ | $\displaystyle 2$ | $\displaystyle 19$ |
| $\displaystyle 1200$-$\displaystyle 1400$ | $\displaystyle 1300$ | $\displaystyle 3$ | $\displaystyle 22$ |
| $\displaystyle 1400$-$\displaystyle 1600$ | $\displaystyle 1500$ | $\displaystyle 1$ | $\displaystyle 23$ |
| $\displaystyle 1600$-$\displaystyle 1800$ | $\displaystyle 1700$ | $\displaystyle 1$ | $\displaystyle 24$ |
| $\displaystyle 24$ |
\[\begin{aligned}
\text { Median }=600 & +\frac{200}{7}(12-6) \\
& =\frac{5400}{7} \text { or } 771 \cdot 4
\end{aligned}
\]
| Rainfall | \(\displaystyle \mathrm{x}_{\mathrm{i}}\) | \(\displaystyle \mathrm{f}_{\mathrm{i}}\) | \(\displaystyle \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}\) |
| $\displaystyle 200$-$\displaystyle 400$ | $\displaystyle 300$ | $\displaystyle 2$ | $\displaystyle 600$ |
| $\displaystyle 400$-$\displaystyle 600$ | $\displaystyle 500$ | $\displaystyle 4$ | $\displaystyle 2000$ |
| $\displaystyle 600$-$\displaystyle 800$ | $\displaystyle 700$ | $\displaystyle 7$ | $\displaystyle 4900$ |
| $\displaystyle 800$-$\displaystyle 1000$ | $\displaystyle 900$ | $\displaystyle 4$ | $\displaystyle 3600$ |
| $\displaystyle 1000$-$\displaystyle 1200$ | $\displaystyle 1100$ | $\displaystyle 2$ | $\displaystyle 2200$ |
| $\displaystyle 1200$-$\displaystyle 1400$ | $\displaystyle 1300$ | $\displaystyle 3$ | $\displaystyle 3900$ |
| $\displaystyle 1400$-$\displaystyle 1600$ | $\displaystyle 1500$ | $\displaystyle 1$ | $\displaystyle 1500$ |
| $\displaystyle 1600$-$\displaystyle 1800$ | $\displaystyle 1700$ | $\displaystyle 1$ | $\displaystyle 1700$ |
| $\displaystyle 24$ | $\displaystyle 20400$ |
Mean \(\displaystyle =\frac{20400}{24}=850\)
(iii)
Sub-divisions having good rainfall \(\displaystyle =2+3+1+1=7\).
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