Question

The weight of coffee (in gm) in 70 packets is given below.

Weight(in gm)	200-201	201-202	202-203	203-204	204-205	205-206
No. of packets	12	26	20	9	2	1

Determine the modal weight of coffee in the packets.

Answer 1

Weight (in gm)	No. of packets (frequency)
200-201	$12\to f_1$
201-202	$26\to f_m$
202-203	$20\to f_2$
203-204	9
204-205	2
205-206	1

Here, the maximum frequency f_m is 26. So, the corresponding modal class is 201-202.
Mode = L+$\left[\frac{f_m-f_1}{2f_m-f_1-f_2}\right]h$
Here, L = lower limit of the modal class =201
$f_m=$maximum frequency = 26
$f_1=$frequency of pre-modal class = 12
$f_2=$frequency of post-modal class = 20
h = width of modal class = 1
$$\begin{gathered} \therefore \mathrm{Mode}=201+\left[\frac{26-12}{2\left(26\right)-12-20}\right]\times 1 \\ =201+\left[\frac{14}{52-32}\right] \\ =201+\frac{14}{20} \\ =201+0.7 \\ =201.7 \\ \therefore \mathrm{The}\mathrm{modal}\mathrm{weight}\mathrm{of}\mathrm{coffee}\mathrm{in}\text{the}\mathrm{packets}\mathrm{is}201.70\mathrm{gm}. \end{gathered}$$