Question

The point of intersection of the 'less than' and the 'more than' ogive corresponds to

• A. Arithmetic mean
• B. Geometric mean
• C. Harmonic mean
• D. Median

Hint:

To find the median graphically, plot both ogives on the same scale. The abscissa (X-value) of their intersection point gives the median directly, while the ordinate (Y-value) gives $N/2$.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
An ogive, or cumulative frequency polygon, is a graphical representation of cumulative frequency distributions.
There are two types of ogives: the "less than" ogive and the "more than" ogive.

Step 2: Detailed Explanation:
The "less than" ogive is constructed by plotting the upper class limits on the horizontal axis and the corresponding cumulative frequencies on the vertical axis.
The "more than" ogive is constructed by plotting the lower class limits on the horizontal axis and their corresponding cumulative frequencies on the vertical axis.
The "less than" ogive rises from left to right, while the "more than" ogive falls from left to right.
When plotted on the same graph, these two curves intersect at a unique point.
At this point of intersection, the cumulative frequency is exactly equal to half of the total frequency ($N/2$).
Projecting this point of intersection down to the horizontal axis (X-axis) yields the value that divides the dataset into two equal halves.
By definition, this value is the median of the distribution.

Step 3: Final Answer:
The point of intersection of the two ogives corresponds to the Median.