Number of mangoes 
Number of boxes (f_{i}) 
50  52 
15 
53  55 
110 
56  58 
135 
59  61 
115 
62  64 
25 
We may observe that the class intervals are not continuous. There is a gap between two class intervals so we have to add \(\frac{1}{2}\) from lower class limit of each interval.
Class size (h) of this data = 3
Now taking 57 as assumed mean,
we can calculate as follows:
Class interval 
f_{i} 
x_{i} 
d_{i} = x_{i}  57 
u_{i} = \(\frac{xi57}{h}\) 
f_{i}u_{i} 
49.5  52.5 
15 
51 
6 
2 
30 
52.5  55.5 
110 
54 
3 
1 
110 
55.5  58.5 
135 
57 
0 
0 
0 
58.5  61.5 
115 
60 
6 
1 
115 
61.5  64.5 
25 
63 
3 
2 
50 

N = 400 



\(\sum\)f_{i}u_{i }= 25 
Mean = A + \(\frac{\sum f_iu_i}{N}\times h\)
\(=57+\frac{25}{400}\times3\)
\(57+\frac{3}{16}\)
\(=57+0.1875=57.1875\)
\(=57.16\)
Number of mangoes kept in packing box is 57.19