Question

The following table shows the frequency distribution of body weight (in gms) of fish in a pond.
Find modal weight of fish in a pond.

Body Weight (in gms)	15 - 15.9	16 - 16.9	17 - 17.9	18 - 18.9	19 - 19.9	20 - 20.9
No. of fish	2	4	8	6	6	4

• A. $16.61$ gms
• B. $17.61$ gms
• C. $18.61$ gms
• D. $19.61$gms

Answer 1

Answer: (B)

$17.61$ gms

Consider the following table to calculate mode:

$ci$	$f_i$
14.95-15.95	2
15.95-16.95	4
16.95-17.95	8
17.95-18.95	6
18.95-19.95	6
19.95-20.95	4

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

Here,

maximum frequency $f_1=8$

$\Rightarrow$ modal class $=16.95-17.95$

lower limit of modal class $l=16.95$

class size $h=1$

preceding frequency of modal class $f_0=4$

succeeding frequency of modal class $f_2=6$

$\therefore Mode=16.95+(\frac{8-4}{16-4-6})\times 1$

$\therefore Mode=16.95+(\frac{4}{6})\times 1$

$\therefore Mode=17.61$

Hence, option $B$ is correct.