236 views

Find the mode of the following data :

$\begin{array}{|cl|cI|}\hline &\text{Age} & \text{0-6} & \text{6-12} & \text{12-18} & \text{18-24} & \text{24-30} & \text{30-36} & \text{36-42} \\ \hline &\text{Frequency} & \text{6} & \text{11} & \text{25} & \text{35} & \text{18} & \text{12} & \text{6} \\ \hline \end{array}$

1. $20.22$
2. $19.47$
3. $21.12$
4. $20.14$

$\text{Mode of the grouped data can be found in the following formula:}$

$\text{Mode=l+($\frac{f_1-f_0}{2f_1-f_0-f_2})*h$}$

where

$\text{l= lower limit of modal class}$

$\text{h=Size of class}$

$\text{$f_0$=Frequency of the class preceding the modal class}$

$\text{$f_1$=Frequency of the modal class}$

$\text{$f_2$=Frequency of the class succeeding the modal class}$

Here The maximum class frequency is $35$ and the class interval corresponding to this frequency is $18-24$. Thus, the modal class is $18-24$

$\therefore$ $\text{Mode=18+$(\frac{35-25}{2*35-25-18})*6$}$.

$\text{Mode=18+$(\frac{10}{70-25-18})*6$}$

$\text{Mode=18+$\frac{60}{27}$=20.22}$

Option $A$ is correct here.
4.7k points

1
357 views
2
370 views