Question

The marks obtained by the sudents of a class, in an exam which was out of 50 marks,is given below.

$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ 5& 1\\ 7& 2\\ 11& 2\\ 16& 3\\ 21& 5\\ 24& 6\\ 28& 3\\ 32& 5\\ 34& 8\\ 39& 6\\ 43& 4\\ 45& 2\\ 49& 3\end{array}$

(i)Find mode for the ungrouped data.

(ii) Represent the same as grouped data, with class intervals of width = 10 and find the mode for the grouped data.

Answer 1

The mode for the ungrouped data is the most frequent observation, which is 34.

Grouped data:

$\begin{array}{cc}\text{Class Intervals}& \text{Frequency}\\ 0-10& 3\\ 10-20& 5\\ 20-30& 14\\ 30-40& 19\\ 40-50& 9\end{array}$

Modal Class is 30-40.

Mode$=I+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$

$=30+\frac{19-14}{38-14-9}\times 10=33.33$