In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying numbers of mangoes. The following was the distribution of mangoes according to the number of boxes:<p></p> <table> <thead> <tr> <th>Number of mangoes</th> <th>Number of boxes</th> </tr> </thead> <tbody><tr> <td>50-52</td> <td>15</td> </tr> <tr> <td>53-55</td> <td>110</td> </tr> <tr> <td>56-58</td> <td>135</td> </tr> <tr> <td>59-61</td> <td>115</td> </tr> <tr> <td>62-64</td> <td>25</td> </tr> </tbody></table> <p>Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?</p>

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

No. of mangoes	Mid - value(xi)	Frequency(fi)	ui=xi-60/3	fiui
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	1	25
Total		400		-375

Here, we have used the exclusive method in class interval formation. If we make the series an inclusive one, the mid-values remain the same. So there is no need to convert the series.

Let's take the assumed mean, A as 60
Class interval = 3 ∴ ui = (xi - 60)/3

̄x = A + h Σfiui / Σfi = 60 + 3 × -375 / 400 = 57.1875

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

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