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Question

In a 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.
Number of mangoes
$$50-5$$2
$$53-5$$5
56-58
$$59-6$$1
$$62-64$$
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?


Solution

 No. of mangoes Mid - value
$$(x_i)$$
 Frequency
$$(f_i)$$
$$u_i = \dfrac{x_i-60}{3}$$ $$f_iu_i$$ 
 50 - 52 51 15 -3 -45
 53 - 55 54 110 -2 -220
 56 - 58 57 135 -1 -135
 59 - 61  60 115 0 0
 62 - 64 63 25 3 25
 Total  400  -375
Here, we have used exclusive method in class interval formation. 
If we make the series an inclusive one the mid-values remain same. 
So there is no need to convert the series.

Lets take assumed mean, $$A$$ as $$60$$
Class interval $$=3$$

$$\therefore  u_i = \dfrac{x_i-A}h = \dfrac{x_i - 60}{3}$$

$$\bar x = A+h\dfrac{\sum f_iu_i}{\sum f_i} = 60 + 3\times \dfrac{-375}{400} = 57.1875$$

Hence, the mean number of mangoes kept in a packing box is $$57.19$$

Mathematics

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