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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?


Solution

Number of mangoes

Number of boxes fi

50 − 52

15

53 − 55

110

56 − 58

135

59 − 61

115

62 − 64

25

It can be observed that class intervals are not continuous. There is a gap of 1 between two class intervals. Therefore, has to be added to the upper class limit and has to be subtracted from the lower class limit of each interval.

Class mark (xi) can be obtained by using the following relation.

Class size (h) of this data = 3

Taking 57 as assumed mean (a), di, ui, fiui are calculated as follows.

Class interval

fi

xi

di = xi − 57

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

3

1

115

61.5 − 64.5

25

63

6

2

50

Total

400

     

25

It can be observed that

Mean number of mangoes kept in a packing box is 57.19.

Step deviation method is used here as the values of fi, di are big and also, there is a common multiple between all di.


Mathematics
Math
Standard X

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