Question

The marks obtained by the students of a class , in a exam which was out of 50 mark 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 the mean for the ungrouped data.

(ii) Represent the same data as grouped data, with class interval of width = 10

Answer 1

$\begin{array}{ccc}{x}_i& f_i& f_i{x}_i\\ 5& 1& 5\\ 7& 2& 14\\ 11& 2& 22\\ 16& 3& 48\\ 21& 5& 105\\ 24& 6& 144\\ 28& 3& 84\\ 32& 5& 160\\ 34& 8& 272\\ 39& 6& 234\\ 43& 4& 172\\ 45& 2& 90\\ 49& 3& 147\end{array}$

$\sum f_i=50$ $\sum f_i{x}_i=1497$

Mean
$=\frac{1497}{50}$

$=29.94$
$\begin{array}{cc}Marks& Numberofstudents\\ 0-10& 3\\ 10-20& 5\\ 20-30& 14\\ 30-40& 19\\ 40-50& 9\end{array}$