Question

Following is the distribution of marks of 70 students in a periodical test:

Marks	Number of students
Marks less than 10 Marks less than 20 Marks less than 30 Marks less than 40 Marks less than 50	3 11 28 48 70

Draw a cumulative frequency curve for the above data and find the median.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{plot}\mathrm{the}\mathrm{points}\mathrm{A}(10,3),\mathrm{B(20,11),}\mathrm{C(30,28),}\mathrm{D(40,48)}\mathrm{and}\mathrm{E(50,70)\; .} \\ \mathrm{Join}\mathrm{AB,}\mathrm{BC,}\mathrm{CD,}\mathrm{DE}\mathrm{and}\mathrm{EA}\mathrm{with}\mathrm{a}\mathrm{free}\mathrm{hand}\mathrm{to}\mathrm{get}\mathrm{the}\mathrm{curve}\mathrm{representing}\mathrm{the}\text{'}\mathrm{less}\mathrm{than}\mathrm{type}\text{'}\mathrm{series}. \end{gathered}$$




​$$\begin{gathered} \mathrm{From}\mathrm{P(0,35)},\mathrm{draw}\mathrm{PQ\; \parallel x}-\mathrm{axis}\mathrm{meeting}\mathrm{the}\mathrm{curve}\mathrm{at}\mathrm{Q.} \\ \mathrm{Draw}\mathrm{QM\perp OX}\mathrm{meeting}\mathrm{the}\mathrm{x-axis}\mathrm{a}\mathrm{t}\mathrm{M.} \\ \mathrm{C}\mathrm{learly},\mathrm{OM=\; 33.5}\mathrm{u}\mathrm{nits.} \\ \mathrm{Hence},Median=33.5 \end{gathered}$$