Median of Grouped Data Questions in English

(A) To construct a 'less than' type Ogive,we plot the cumulative frequencies against the upper class limits of the respective class intervals.
Therefore,the upper limits of the classes are represented on the $X$-axis and the corresponding cumulative frequencies are represented on the $Y$-axis.

(A) The median of a frequency distribution can be determined graphically by drawing both the 'less than' type and 'more than' type Ogives.
The point of intersection of these two Ogives provides the median value.
The $x$-coordinate of this intersection point represents the median of the data,while the $y$-coordinate represents the cumulative frequency corresponding to the median.
Given that the intersection point is $(20, 25)$,the $x$-coordinate is $20$.
Therefore,the median of the data is $20$.

(B) The cumulative frequency distribution is a statistical tool used to determine the median of a dataset.
To calculate the median,we first find the cumulative frequencies of the given data.
Then,we identify the median class by finding the value $N/2$,where $N$ is the total frequency.
The median is then calculated using the formula: $\text{Median} = l + \left( \frac{\frac{N}{2} - cf}{f} \right) \times h$,where $cf$ is the cumulative frequency of the class preceding the median class.
Therefore,the correct option is $B$.