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50 students enter for a school javeloin ...

50 students enter for a school javeloin throw competition. The distance (in metre) thrown are recorded below

(i) Construct a cumulative frequency table.
(ii)Calculate the median distance by using the formula for median.

Text Solution

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To draw less than type ogive, we plot the points (0,0),(20,6),(40,17),(60,34),(80,46), (100,50) join the all these points by free hand

Taking Y=25cm on Y-axis and draw a line parallel to X-axis, which meets the curve at point A. From points A, we draw a line perpendicular to X-axis, where this meets that point is the required median i.e.49.4
(iii) Now, `(N)/(2)=(50)/(2)=25`
Which lies is the interval 40-60 l=40, h=20, cf=17 and f=17
`"Median"=l+(((N)/(2)-cf))/(f)xxh`
`40+((25-17))/(17)xx20`
`=40+(8 xx20)/(17)`
`=40+9.41`
`=49.41`
(iv) Yes, median distane calculated by parts, (ii) and (iii) are same.
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