Question

The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its:
A.mean
B.median
C.mode
D.all of the above

Answer 1

Hint: The curves of more than type and less than type intersect at only one point, which is their middle value or median. The reason for this is that the middle value of a given data is the same irrespective of the type of cumulative frequency we consider.

Complete step-by-step answer:
Median is the middle value in a set of data. When we plot a graph of more than type than the value of cumulative frequency decreases from maximum to minimum and in case of less than type, it increases from minimum value to maximum value. However irrespective of the type of cumulative frequency, both the curves have a common middle value which is at the point which is exactly half of total cumulative frequency.
So, when both these curves are plotted together, we get an intersection point which gives us the median of the data.
Option B is correct answer.

Note: Abscissa of a graph means the x-coordinate of a point as in the curve plotted the data is on x-axis. Intersection of the more than and less type curve give the median irrespective of nature of the data, that is it doesn’t matter if the data is even or not. This is because the middle value of the data depends only on its position from both the end that it should be in the middle.