Question

The India Meteorological Department observer seasonal and annual rainfall every year in different sub-divisions of our country. It helps them to compare and analyze the results. 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:

1. Write the modal class.    (1)
2. 1. Find the median of the given data.    (2)
                                   OR
   2. Find the mean rainfall in the season.    (2)
3. 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?    (1)

Answer 1

Rainfall (mm)	No. of Sub-divisions	c.f	xi	fixi
200 − 400	3	3	300	900
400 − 600	4	7 → cf	500	2000
600 − 800	7 → f	14	700	4900
800 − 1000	4	18	900	3600
1000 − 1200	3	21	1100	3300
1200 − 1400	3	24	1300	3900
	N = 24			∑fixi = 18600

(i) Highest frequency = 7

∴ modal class = 600 − 800

N = 24

`N/2 = 24/2`

= 12

(ii) (a) cf just greater then `N/2` (12) is 14

∴ 600 − 800        ...(Median class)

Lower value (l) = 600, frequency (f) = 7, (cf) = 7

Median = `l + ((N/2) - cf)/f xx h`

= `600 + (12 - 7)/7 xx 200`

= `600 + 1000/7`

= 600 + 142.8

= 742.8

(b) `barx = (sumf_ix_i)/(sumf_i)`

= `18600/24`

= 775

(iii) Good rainfall ≥ 800

= 800 − 1000, 1000 − 1200, 1200 − 1400

= 4 + 3 + 3

= 10