Question

Following table gives frequency distribution of electricity consumption of a household in certain area in a month.

No. of units of electricity	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100
No. of households	4	16	47	65	8

Find modal no. of units of electricity consumed by households in a month.

• A. $64$
• B. $62.8$
• C. $63.8$
• D. None of these

Answer 1

Answer: (D)

None of these

Frequency distribution table:

$ci$	$f_i$
$0-20$	$4$
$20-40$	$16$
$40-60$	$47$
$60-80$	$65$
$80-100$	$8$

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

Here,

maximum frequency $f_1=65$

$\Rightarrow$ modal class $=60-80$

lower limit of modal class $l=60$

class size $h=20$

preceding frequency of modal class $f_0=47$

succeeding frequency of modal class $f_2=8$

$\therefore Mode=14.05+(\frac{65-47}{130-47-8})\times 20$

$\therefore Mode=14.05+(\frac{18}{75})\times 20$

$\therefore Mode=64.8$

Hence, option $D$ is correct.