Question

An aircraft has 120 passenger seats. The number of seats occupied during 100 fights is given below :

No. of seats	100-104	104-108	108-112	112-116	116-120
Frequency	15	20	32	18	15

Determine the mean of seats occupied over the flights

Answer 1

Class interval	Class Marks $\left(x_i\right)$	Frequency $\left(f_i\right)$	Deviation $(d_i=x_i-a)$	$f_i{d}_i$
100-104	102	15	-8	-120
104-108	106	20	-4	-80
108-112	110	32	0	0
112-116	114	18	4	72
116-120	118	15	8	120
		$N=\sum f_i=100$		$\sum f_i{d}_i=-8$

$\therefore$ Assumed mean, $a=110$

Class width $h=4$

and total observation, $N=100$

Hence, finding mean

$Mean\left(\overline{x}\right)=a+\frac{\sum f_1{d}_1}{\sum f_1}$

$=110+(-8/100)$

$=110-0.08$

$=109.92$

But we know that the seats cannot be in decimal

Therefore, the no, of seats $=109$.