Question

The weight of coffee in $70$ packets are shown in the following table :

Weight (in g)	Number of packets
$200-201$	$12$
$201-202$	$26$
$202-203$	$20$
$203-204$	$9$
$204-205$	$2$
$205-206$	$1$

Determine the modal weight .

Answer 1

Finding the modal weight:

We know that formula for calculating the modal weight is

Mode$=\text{l+(}\frac{{\text{f}}_1{\text{-f}}_0}{2{\text{f}}_1{\text{-f}}_0{\text{-f}}_2}\text{)×h}$

Where $\text{l}$is the lower limit of the modal class and $\text{h}$is the class -width

${\text{f}}_1$ is the frequency of modal class $,{\text{f}}_0$ is the frequency of the previous class of the modal class and ${\text{f}}_2$is the frequency of the next class to the modal class .

So first we choose the modal class.

The class whose frequency is highest is called the modal class .

So $\text{202-203}$ is the modal class because its frequency is highest that is $26$.

Here ${\text{f}}_1{\text{=26,f}}_0{\text{=12,f}}_2\text{=20}$ and $\text{l=201,h=202-201=1}$

So mode $$\begin{gathered} =201+\left(\frac{26-12}{2\left(26\right)-12-20}\right)\times 1 \\ =201+\left(\frac{14}{52-32}\right)\times 1 \\ =201+\left(\frac{14}{20}\right)\times 1 \\ =201+\left(\frac{14}{20}\right) \\ =\frac{201\times 20+14}{20}=\frac{4034}{20}=201.70 \end{gathered}$$

Hence, modal weight of the given data is $\text{201.70 g}$