Question

The median of a given frequency distribution is found graphically with the help of:

• A. Histogram
• B. Pie Chart
• C. Bar graph
• D. Ogive

Hint:

Keep these graphical relationships in mind:
- Histogram \(\implies\) Mode
- Ogive \(\implies\) Median (and other partition values like Quartiles and Percentiles)

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Statistical data can be represented graphically using various charts and curves.
Certain graphs are specifically designed to help estimate partition values (such as the median, quartiles, deciles, and percentiles) without performing manual calculations.

Step 3: Detailed Explanation:
Let us evaluate each of the given graphical methods:
- Option (A) Histogram:
A histogram is a bar-like representation of continuous grouped data, where the area of each bar is proportional to the class frequency.
While a histogram is used to find the mode of a distribution graphically, it is not used to find the median.
- Option (B) Pie Chart:
A pie chart represents categorical or relative data as sectors of a circle.
It shows proportions of a whole, but cannot be used to find cumulative statistics like the median.
- Option (C) Bar graph:
A bar graph represents discrete categorical data using rectangular bars. It does not display cumulative data.
- Option (D) Ogive:
An ogive is a cumulative frequency polygon. There are two types:
1. "Less than" ogive: plotted by pairing upper class limits with cumulative frequencies.
2. "More than" ogive: plotted by pairing lower class limits with cumulative frequencies.
By plotting both curves on the same axes, they intersect at a point.
The x-coordinate of this intersection point corresponds to the value of the median.
Alternatively, we can locate the value \(\frac{N}{2}\) on the y-axis, draw a horizontal line to intersect the single ogive, and drop a perpendicular to the x-axis to read the median value.
Thus, the median is found graphically using an Ogive.

Step 4: Final Answer:
Therefore, the correct option is (D).