Question

The marks obtained by 30 students in a class assessment of 5 marks is given below:
$$\begin{array}{ccccccc}Marks& 0& 1& 2& 3& 4& 5\\ No.ofStudents& 1& 3& 6& 10& 5& 5\end{array}$$\)
Calculate the mean, median and mode of the above distribution. [3 MARKS]

Answer 1

Mean, Median and Mode : 3 Marks

$\begin{array}{cccc}Marks& No.ofstudents& f_i{x}_i& c.f.\\ 0& 1& 0& 1\\ 1& 3& 3& 4\\ 2& 6& 12& 10\\ 3& 10& 30& 20\\ 4& 5& 20& 25\\ 5& 5& 25& 30\\ & \sum f_i=30& \sum f_i{x}_i=90& \end{array}$
Mean $=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{90}{30}=3$
Median $=\frac{{\left(\frac{n}{2}\right)}^{thobservation}+{(\frac{n}{2}+1)}^{thobservation}}{2}$
$=\frac{{15}^{th}+{16}^{thobservation}}{2}=\frac{3+3}{2}=3$
Mode = highest frequency observation
=3