Question

An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table:

Number of seats	100 – 104	104 – 108	108 – 112	112 – 116	116 – 120
Frequency	15	20	32	18	15

Answer 1

We first, find the class mark x_i of each class and then proceed as follows.

Number of seats	Class marks `(bb(x_i))`	Frequency `(bb(f_i))`	Deviation `bb(d_i = x_i - a)`	`bb(f_i d_i)`
100 – 104	102	15	– 8	– 120
104 – 108	106	20	– 4	– 80
108 – 112	a = 110	32	0	0
112 – 116	114	18	4	72
116 – 120	118	15	8	120
		`N = sumf_i = 100`		`sumf_i d_i = -8`

∴ Assumed mean, a = 110

Class width, h = 4

And total observations, N = 100

By assumed mean method, 

Mean `(barx) = a + (sumf_i d_i)/(sumf_i)`

= `110 + ((-8)/100)`

= 110 – 0.08

= 109.92

But seats cannot be in decimal, so number of seats is 109.