Marks Conversion into
exclusive series
No. of students Cumulative Frequency
(x)   (f) (C.M)
410-419 409.5-419.5 14 14
420-429 419.5-429.5 20 34
430-439 429.5-439.5 42 76
440-449 439.5-449.5 54 130
450-459 449.5-459.5 45 175
460-469 459.5-469.5 18 193
470-479 469.5-479.5 7 200

The median value of a series may be determinded through the graphic presentation of data in the form of Ogives.This can be done in 2 ways.

1. Presenting the data graphically in the form of 'less than' ogive or 'more than' ogive .
2. Presenting the data graphically and simultaneously in the form of 'less than' and 'more than' ogives.The two ogives are drawn together.

1. Less than Ogive approach

Marks Cumulative Frequency (C.M)
Less than 419.5 14
Less than 429.5 34
Less than 439.5 76
Less than 449.5 130
Less than 459.5 175
Less than 469.5 193
Less than 479.5 200

Steps involved in calculating median using less than Ogive approach -
1. Convert the series into a 'less than ' cumulative frequency distribution as shown above .
2. Let N be the total number of students who's data is given.N will also be the cumulative frequency of the last interval.Find the (N/2)th item(student) and mark it on the y-axis.In this case the (N/2)th item (student) is 200/2 = 100th student.
3. Draw a perpendicular from 100 to the right to cut the Ogive curve at point A.
4.From point A where the Ogive curve is cut, draw a perpendicular on the x-axis. The point at which it touches the x-axis will be the median value of the series as shown in the graph.


More than Ogive approach

Marks Cumulative Frequency (C.M)
More than 409.5 200
More than 419.5 186
More than 429.5 166
More than 439.5 124
More than 449.5 70
More than 459.5 25
More than 469.5 7
More than 479.5 0

Steps involved in calculating median using more than Ogive approach -
1. Convert the series into a 'more than ' cumulative frequency distribution as shown above .
2. Let N be the total number of students who's data is given.N will also be the cumulative frequency of the last interval.Find the (N/2)th item(student) and mark it on the y-axis.In this case the (N/2)th item (student) is 200/2 = 100th student.
3. Draw a perpendicular from 100 to the right to cut the Ogive curve at point A.
4.From point A where the Ogive curve is cut, draw a perpendicular on the x-axis. The point at which it touches the x-axis will be the median value of the series as shown in the graph.

2.Less than and more than Ogive approach

Another way of graphical determination of median is through simultaneous graphic presentation of both the less than and more than Ogives.

1.Mark the point A where the Ogive curves cut each other.
2.Draw a perpendicular from A on the x-axis. The corresponding value on the x-axis would be the median value.

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