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50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below:

Distance(in m)
0-20
20-40
40-60
60-80
80-100
Number of students
6
11
17
12
4

Draw a cumulative frequency (less than type) curve and calculate the median distance thrown by using this curve.

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45.1m

49.4m

45.6m

43.6m

answer is B.

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Detailed Solution

Given the data of 50 students enter for a school javelin throw competition.

Distance(in m)	0-20	20-40	40-60	60-80	80-100
Number of students	6	11	17	12	4

The cumulative distribution table is,

Distance (in m)	Frequency	Cumulative frequency
0	0	0
Less than 20	6	6
Less than 40	11	17
Less than 60	17	34
Less than 80	12	46
Less than 100	4	50

To draw less than type ogive, plot the points (0,0), (20,6), (40,17), (60,34), (80,46), (100,50) and join them. Now,

N 2 = 502 = 25

Taking y equal to 25 on y-axis, draw a line parallel to x-axis, which meet the curve at a point. From that point, draw a line perpendicular to x-axis, where this meets that point at 49.4.

https://lh5.googleusercontent.com/i5nEFwfz_ZAfYb0mQsQf84OfuoIFrmrmNTFy9BLLaDodBTO8FgWBDQwV4tjoBmsDLI0bTPty8OpZxgDiRzGtBvETJRsZAjFTcPwk6Efv_PpsqJhr5EgQZ4ar-TR9rJ9_W7NvmDrb_GCL17DjI4U23DfiAsmZ2a_xhfPSOxivHmLNN5qbQM3S7S3udDhtHLkvUTigmi8hMw

Hence, the required median is 49.4.
Therefore, the correct answer is option (2).

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