Question

The First case of covid-19 pandemic in Sikkim state was reported on 23rd May, 2020. The number of covid-19 cases of various days are given below: DAYS NO. OF CASES Less than 30 1 Less than 60 85 Less than 90 639 Less than 120 1475 Less than 150 2568 Less than 180 3831 Less than 210 4650 (a) Find the mean, mode and median of above data (b) Find the probability of (i)No. of cases from 30-60 days. (ii) No. of cases from above 180 days.

Answer 1

Given :  The number of covid-19 cases of various days of Sikkim

To Find :  (a) Find the mean, mode and median of above data

(b) Find the probability of

(i)No. of cases from 30-60 days.

(ii) No. of cases from above 180 days.

Solution:

Class        f            cf            Mean   d= (mean - 105)/30   d * f

0 - 30       1              1            15         -3                               -3

30 - 60    84           85         45        -2                               -168

60 - 90    554       639       75         -1                               -554

90-120    836       1475       105        0                               0

120-150   1093      2568      135        1                               1093

150-180    1263      3831      165         2                              1263

180 - 210   819       4650     195         3                             2457

                4650                                                                4,088

Mean = 105  +  30 x ( 4008)/4650

= 105 + 25.86

= 130.86

4650/2 = 2325

Median =  120  + 30 x (2325 - 1475)/1093

= 120 + 23.33

= 143.33

Mode = 150 + 30 ( 1263 - 1093)/(1263 - 1093 + 1263 - 819)

= 150 + 30 ( 170)/(614)

= 150 + 8.3

= 158.3

probability of (i)No. of cases from 30-60 days = 84 /4650 = 0.0181

probability of No. of cases above 180 days. = 819 /4650 = 0.1761

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