Answer :
Let us prepare table for cumulative frequencies for curve 1 and 2
(i) For curve 1 first cumulative frequency is least and last one is highest. Hence, it less than type ogive. Whereas for curve 2 first cumulative frequency is heighest and last one is least. Hence, it greater than type ogive.
(ii) Calculation of median :
Here, total frequency = ∑ fi = N = 66
cumulative frequency just greater than or equal to 33 is 40.
Therefore, corresponding class, 20 -30 is a median class.
Here, L = 20, c.f. = 32, h = 10, f = 8
∴ Median = 20 + 1.25
∴ Median = 21.25
Hence, median rainfall of Dispur is 21.25 cm.
(iii) Mean rainfall = 23.4 cm
We know that,
Mean – Mode = 3 (Mean – Median)
∴ 23.4 – Mode = 3 (23.4 – 21.25)
∴ 23.4 – Mode = 3 (2.15)
∴ 23.4 – Mode = 6.45
∴ Mode = 23.4 – 6.45
∴ Mode = 16.95
Hence, Modal rainfall of Dispur is 16.95 cm.
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