India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country.

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It helps them to compare and analyse the results. The table give

Question

India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country.

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It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018:

| Rainfall (mm) | Number of Sub-divisions |
|---------------|------------------------|
| $200$-$400$ | $2$ |
| $400$-$600$ | $4$ |
| $600$-$800$ | $7$ |
| $800$-$1000$ | $4$ |
| $1000$-$1200$ | $2$ |
| $1200$-$1400$ | $3$ |
| $1400$-$1600$ | $1$ |
| $1600$-$1800$ | $1$ |

Based on the above information, answer the following questions:
(I) Write the modal class.
(II) Find the median of the given data.

OR

(II) Find the mean rainfall in this season.
(III) If sub-division having at least 1000 mm rainfall during monsoon season, is considered good rainfall sub-division, then how many sub-divisions had good rainfall?

Accepted Answer

Step 1: (i) Modal Class is $600$-$800$
Step 2: (ii) $\frac{N}{2} = 12$, median class $= 600$-$800$

| Rainfall | $x_i$ | $f_i$ | $cf$ |
|----------|-------|-------|------|
| $200$-$400$ | $300$ | $2$ | $2$ |
| $400$-$600$ | $500$ | $4$ | $6$ |
| $600$-$800$ | $700$ | $7$ | $13$ |
| $800$-$1000$ | $900$ | $4$ | $17$ |
| $1000$-$1200$ | $1100$ | $2$ | $19$ |
| $1200$-$1400$ | $1300$ | $3$ | $22$ |
| $1400$-$1600$ | $1500$ | $1$ | $23$ |
| $1600$-$1800$ | $1700$ | $1$ | $24$ |
Step 3: Median $= 600 + \frac{200}{7}(12 - 6)$
$= \frac{5400}{7}$ or $771.4$
Step 4: (iii) Sub-divisions having good rainfall $= 2 + 3 + 1 + 1 = 7$

Question

Solution