What determines the point of intersection of two cumulative frequency curves ?

Question

Accepted Answer

The correct option is 1:
The intersection point of two cumulative frequency curves is the graphical method for determining the Median of a data set. A cumulative frequency curve, also known as an Ogive, can be constructed in two ways: the 'less than' ogive (plotting cumulative frequency against the upper class boundaries) and the 'more than' ogive (plotting cumulative frequency against the lower class boundaries). When both the 'less than' and 'more than' ogives for the same data distribution are plotted on the same graph, the point where they intersect corresponds to the value of the variable on the horizontal axis that splits the data into two equal halves. By definition, this central value, which divides the data into 50% above and 50% below, is the Median. The corresponding value on the vertical axis at this intersection point will be N/2 (half of the total number of observations).

The incorrect option is 2:
Mode is the value that occurs most frequently in a data set. Graphically, the Mode is determined by using a Histogram, specifically by drawing lines from the top corners of the highest bar (the modal class) to the adjacent corners of the neighboring bars.

The incorrect option is 3:
Mean is the arithmetic average of a data set. The Mean is calculated mathematically by summing all observations and dividing by the total number of observations; it cannot be determined directly by finding the intersection of the two cumulative frequency curves.

The incorrect option is 4:
Q3 stands for the Third Quartile, which is the value that separates the highest 25% of the data from the lowest 75%. While quartiles can be found using a single cumulative frequency curve, they are determined by finding the value corresponding to 3N/4 on the vertical axis, not by the intersection of the 'less than' and 'more than' curves.