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 = 100^{th }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 = 100^{th }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.

ssasd