What is the inter-quartile range of the above distribution?

Step 1: First quartile of the distribution (Question 27)

Total number of students $n=50$.

Position of the first quartile: $\frac{n+1}{4}=\frac{51}{4}=12.75$.

From the cumulative frequency curve, a cumulative frequency of $12.75$ corresponds to $35$ marks.

First quartile $= 35$ marks.
35 marks

Step 2: Modal class of the distribution (Question 28)

The modal class is the class interval in which the cumulative frequency curve has the steepest slope (highest frequency).

From the graph, the greatest rise occurs between $50$ marks and $60$ marks.

Modal class = 50{-60 marks.}
50-60 marks

Step 3: Probability that a student gets $50$ or more marks (Question 29)

From the graph, cumulative frequency up to $50$ marks $=25$.

Number of students getting $50$ or more marks $=50-25=25$.

Probability $=\frac{25}{50}=\frac{1}{2}$.

Probability =\dfrac{1{2}.}
\dfrac{1{2}}

Step 4: Number of students who got $75$ marks or more (Question 30)

From the graph (near upper quartile), cumulative frequency up to $75$ marks $=38$.

Number of students getting $75$ marks or more $=50-38=12$.

$12$ students.
12 students