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# 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 50-52 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?

Since, the given data is not continuous so we add 0.5 to the upper limit and subtract 0.5 from the lower limit as the gap between two intervals are 1

Here, assumed mean (A) = 57, Class size (h)
= 3

Here, the step deviation is used because the frequency values are big.

 Class Interval Number of boxes $$(f_i)$$ Mid-point $$(x_i)$$ $$d_i \ = \ x_i \ - \ A$$ $$f_i d_i$$ 49.5-52.5 15 51 -6 90 52.5-55.5 110 54 -3 -330 55.5-58.5 135 57 0 0 58.5-61.5 115 60 3 345 61.5-64.5 25 63 6 150 $$\sum f_i \ = \ 400$$ $$\sum f_i d_i \ = \ 75$$

The formula to find out the Mean is:

$$\overline{x} \ = \ A \ + h \frac{ \sum \ f_i d_i}{ \sum f_i} \ = \ 57 \ + \ 3 × \frac{75}{400}$$

$$= \ 57 \ + \ 0.1875 \ = \ 57.19$$

$$\therefore$$ The mean number of mangoes kept in a packing box is 57.19