The table below shows the marks obtained by forty pupils in a Mathematics test. Marks 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 59 No of pupils 4 5 6 12 8 ...

(a) Histogram

Use continuous class boundaries. Since all class widths are 10 marks, the bar heights are the frequencies.

(b) Mode

The modal class is \(30-39\), with class boundaries \(29.5-39.5\).

\[\text{Mode}=L+\frac{d_1}{d_1+d_2}\times c\]

\[=29.5+\frac{12-6}{(12-6)+(12-8)}\times10\]

\[=29.5+\frac{6}{10}\times10=\boxed{35.5\text{ marks}}\]

(c) Median

\[N=40,\qquad \frac{N}{2}=20\]

The 20th value lies in the class \(30-39\), since the cumulative frequency rises from \(15\) to \(27\) in this class.

\[\text{Median}=L+\frac{\left(\frac{N}{2}-\text{cumulative frequency before median class}\right)}{f_m}\times c\]

\[=29.5+\frac{20-15}{12}\times10\]

\[=29.5+4.1667=\boxed{33.67\text{ marks}}\]