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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

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