Question

The following table gives the duration of movies in minutes:

Duration	100 – 110	110 – 120	120 – 130	130 – 140	140 – 150	150 – 160
No. of movies	5	10	17	8	6	4

Using step-deviation method, find the mean duration of the movies.

Answer 1

Duration (in minutes)	No. of movies ${\displaystyle f_i}$	${\displaystyle x_i}$	${\displaystyle u_i=\frac{x_i-A}{h}}$	${\displaystyle f_i{u}_i}$
100 – 110	5	105	–3	–15
110 – 120	10	115	–2	–20
120 – 130	17	125	–1	–17
130 – 140	8	135 = A	0	0
140 – 150	6	145	1	6
150 – 160	4	155	2	5
Total	50			–38

${\displaystyle \overline{x}=\frac{\sum f_i{u}_i}{\sum f}\times h}$

= ${\displaystyle 135+\frac{(-38)}{50}\times 10}$

= 135 – 7.6

= 127.4