Question

Ina retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

mangoes	50-52	53-55	56-58	59-61	62-64
No. of boxes	15	110	135	115	25

Mean number of mangoes kept in a packing box is 57.19
If true then enter $1$ and if false then enter $0$

Answer 1

Number of mangoes	Number of boxes $f_i$	Class mark $x_i$	$u_i=\frac{x_i-57}{3}$	$f_i\times u_i$
50-52	15	51	-2	-30
53-55	110	54	-1	-110
56-58	135	57 = a	0	0
59-61	115	60	1	115
62-64	25	63	2	50
Total	$n=400$			25

$a=57,h=2,n=400$ and $\sum f_i{u}_i=25$.
By step deviation method,
$mean=a+h\times \frac{1}{n}\times \sum f_i{u}_i=57+2\times \frac{1}{400}\times 25=57.19$