notes
In this concept we will study about Relation of Ogive and Median. These graphical representation of the frequency distribution are called Ogives. Actual limits are on the x-axis and cumulative frequencies on the y-axis.
Ogive is also known as cumulative frequency distribution.
You will be asked to draw either a less than frequency ogive or more than frequency ogive.
Example: The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution :
Convert the distribution above to a less than type cumulative frequency distribution and also to a more than type cumulative frequency distribution, and draw its ogive.
1) Less than type cumulative frequency table
|
Classes |
cf |
|
Less than 10 |
2 |
|
Less than 15 |
14 |
|
Less than 20 |
16 |
|
Less than 25 |
20 |
|
Less than 30 |
23 |
|
Less than 35 |
27 |
|
Less than 40 |
30
|
2) More than type cumulative frequency table
|
Classes |
cf |
|
More than 5 |
30 |
|
More than 10 |
28 |
|
More than 15 |
16 |
|
More than 20 |
14 |
|
More than 25 |
10 |
|
More than 30 |
7 |
|
More than 35 |
3 |
The graphical representation of both the ogives will be
Here, `N/2= 30/2= 15`
Now, we will take 15 on y axis and draw a perpendicular line that touches the curve, and from the point where the perpendicular touches the curve draw a perpendicular that touches the x axis, the point at which the perpendicular touches the x axis is the median.
Thus, here the Median is 17.5
