Question

Forty persons were examined for their Haemoglobin % in blood (in mg per 100 ml) and the results were grouped as below :
Determine modal value of Haemoglobin % in blood of persons.

Haemoglobins % (mg / 100ml)	13.1 - 14	14.1 - 15	15.1 - 16	16.1 - 17	17.1 - 18
No. of Persons	8	12	10	6	4

• A. $3.71mg/100ml$
• B. $14.71mg/100ml$
• C. $15.71mg/100ml$
• D. $16.71mg/100ml$

Answer 1

Answer: (B)

$14.71mg/100ml$

Consider the following table to calculate mode:

$ci$	$f_i$
13.05-14.05	8
14.05-15.05	12
15.05-16.05	10
16.05-17.05	6
17.05-18.05	4

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

Here,

maximum frequency $f_1=12$

$\Rightarrow$ modal class $=14.05-15.05$

lower limit of modal class $l=14.05$

class size $h=1$

preceding frequency of modal class $f_0=8$

succeeding frequency of modal class $f_2=10$

$\therefore Mode=14.05+(\frac{12-8}{24-8-10})\times 1$

$\therefore Mode=14.05+(\frac{4}{6})\times 1$

$\therefore Mode=14.71$

Hence, option $B$ is correct.