Question

For the given data,
$\begin{array}{ccccccc}\text{Weight (in kg)}& 20& 24& 25& 30& 32& 35\\ \text{Number of students}& 2& 1& 3& 1& 2& 1\end{array}$
the correct option(s) is/are

• A. mean is $27$
• B. median is $25$
• C. mode is $21.4$
• D. median is $26$

Answer 1

Answer: (B), (C)

mode is $21.4$

Create distribution table for the given data.
$\begin{array}{cccc}\text{Weight(in kg)}& \text{No of students}& \text{Cumulative Frequency}& (f_i\times x_i)\\ x_i& f_i& & \\ 20& 2& 2& 40\\ 24& 1& 3& 24\\ 25& 3& 6& 75\\ 30& 1& 7& 30\\ 32& 2& 9& 64\\ 35& 1& 10& 35\\ & N=\sum f_i=10& & N=\sum \left(f_i{x}_i\right)=268\end{array}$
Here, $N=10$ which is even.

Median $=\frac{1}{2}[{\left(\frac{N}{2}\right)}^{th}\text{term}+{(\frac{N}{2}+1)}^{th}\text{term}]$
$=\frac{1}{2}[5^{th}\text{term}+6^{th}\text{term}]$
From cumulative frequency $5^{th}$ and $6^{th}$ term is $25$
$=\frac{1}{2}[25+25]=25$

Mean $=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{268}{10}=26.8$

$\text{Mode}=3\text{(Median)}-2\text{(Mean)}$
$=3\times 25-2\times 26.8=21.4$