Finding Median
Graphically
Marks
inclusive series |
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.
The median turns
out to be 443.94.
2.More than
Ogive approach
| More than 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.
The median turns out to be 443.94.
3.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.
The median turns
out to be 443.94.
|
