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Question

The following table gives the marks obtained by 300 students of a management course. Find the median of the distribution.

Marks obtainedNo. of students
01526
153034
304564
456076
607560
759060
9010010

A
62.96 marks
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B
62.13 marks
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C
50.13 marks
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D
50.96 marks
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Solution

The correct option is C 50.13 marks
Median is the middle most value of a given series that represents the whole class of the series. For a group data,
Median = L + [{(n/2) – B}/G] × w where
  • Lis the lower class boundary of the group containing the median
  • nis the total number of values
  • Bis the cumulative frequency of the groups before the median group
  • Gis the frequency of the median group
  • wis the group width
Since the median is the middle value, which in this case is 165th one , which is in the 45-60 group. Therefore , 45-60 is the median group so
  • L= 45
  • n= 330
  • B= 26 + 34 + 64 = 124
  • G= 76
  • w= 15

Median= 45 + [{(330/2) – 124}/76] × 15

  • = 45 + 8.09
  • = 53.09

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