Question

Fill in the blanks:
In 'Less Than’ Ogive, the cumulative frequencies are written corresponding to the __________[P] limits of the classes of the given data.
In 'More Than' Ogive, the cumulative frequencies are written corresponding to the __________[Q] limit of the classes.
On an ogive, point P whose y-coordinate = \[\dfrac{n}{2}\] (i.e., half of the total number of the entries), has its x-coordinate equal to the ___________[R] of the data.
Two ogives, one 'less than' type and the other 'more than' type for the same data when drawn simultaneously on the same graph, intersect each other at the point P whose ___________[S] = \[\dfrac{n}{2}\] and _____________[T] = median of the data where n is the total number of the entries of the data.
A. P : Upper, Q : Lower, R : Median, S : y – coordinate, T : x – coordinate
B. P : Lower, Q : Upper, R : Median, S : y – coordinate, T : x – coordinate
C. P : Upper, Q : Lower, R : Median, S : x – coordinate, T : y – coordinate
D. P : Upper, Q : Lower, R : Upper limit, S : y – coordinate, T : x – coordinate

Answer 1

Hint: We will first understand and mention what we do in each kind of ogive and then we will just compare them to the given fill in the blanks and thus we get to know the answer to the given question.

Complete step by step solution:
In “Less than” Ogive as the name suggests we need the cumulative frequency of any quantity in less than format. So, we basically need to join upper limits of classes.
$\therefore $ P = Upper limit
In “More than” Ogive as the name suggests we need the cumulative frequency of any quantity in more than format. So, we basically need to join lower limits of classes.
$\therefore $ Q = Lower limit
Now coming to the next blank, we know that the \[{\left( {\dfrac{n}{2}} \right)^{th}}\] term of the sequence is the middle term of the sequence. The middle term is known as median (when sequence is in ascending order).
$\therefore $ R = Median
When both the “less than” and “more than” ogives intersect, they intersect at median because median remains constant for the same set of data taken in any format. Therefore, the x – coordinate will give a median and y – coordinate will be \[\dfrac{n}{2}\] because at that point the median exists.
$\therefore $ S = y – coordinate
$\therefore $ T = x – coordinate

So, the correct answer is “Option B”.

Note: Median is basically the mid – point of the set where the data is set on either ascending or descending order. It gives us some idea about how the data is skewed with respect to the mean of the data.
The students must note that, if they get confused between the blanks, they must try to pick an example for more clarity of the same picture.
The students must note that ogives graphs are generally drawn to know the median of the data. Otherwise, it is not very convenient to read such graphs for data.