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

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.

\textbf{First quartile $= 35$ marks.}
35 marks

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.

\textbf{Modal class $= 50{-}60$ marks.}
50-60 marks

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

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

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

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

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