Question

In the below figure, the value of the median of the data using the graph of less than ogive and more than ogive is
$\left( A \right)5$
$\left( B \right)40$
$\left( C \right)80$
$\left( D \right)15$

Answer 1

Hint: In this particular type of question use the concept that the abscissa i.e. x coordinate of the intersection point of less than ogive and more than ogive is the required median of the data using the graph of less than ogive and more than ogive so use this concept to reach the solution of the question.

Complete step by step solution:
Although the answer of the question is hidden in the question but how it comes lets understand.
The ogive is a free hand graph (i.e. it is drawing by a free hand)
The abscissa i.e. x coordinate of the intersection point of less than ogive and more than ogive is the required median of the data using the graph of less than ogive and more than ogive.
As we see that the marks is on the x-axis that’s why we have taken the abscissa i.e. x coordinate, as the median is of the marks not of the cumulative frequency if not specify, if specify then we have to take the median of the cumulative frequency.
So, we have to take the ordinate i.e. y coordinate.
So from the graph it is clear that the intersection point of less than ogive and more than ogive is P.
So the intersection coordinate P = (15, 40) from the graph.
So in the above coordinate the abscissa is 15.
So the median of the data using the graph of less than ogive and more than ogive = 15.
So this is the required answer.
Hence option (D) is the correct answer.

Note: Whenever we face such types of questions the key concept we have to remember is that the abscissa is x-coordinate and the ordinate is y-coordinate so first find out the intersection point of less than ogive and more than ogive using the graph then the x-coordinate of the intersection point is the required median of the data using the graph of less than ogive and more than ogive.