# In a retail market, fruit vendor were-selling mangoes kept in packing boxes. Number of mangoes: 50 - 52, 53 - 55, 56 - 58, 59 - 61, 62 - 64

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In a retail market, fruit vendor 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.

 Number of mangoes: 50 - 52 53 - 55 56 - 58 59 - 61 62 - 64 Number of boxes: 15 110 135 115 25

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

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 Number of mangoes Number of boxes (fi) 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 fi xi di = xi - 57 ui = $\frac{xi-57}{h}$ fiui 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 $\sum$fiui = 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