The following table gives production yield in kg. per hectare of wheat of 150 farms in a village. Calculate the mean, median and mode values.

Production yield (kg. per hectare)

50 – 53

53 – 56

56 – 59

59 – 62

62 – 65

65 – 68

68 – 71

71 – 74

74 – 77

Number of farms

3

8

14

30

36

28

16

10

5

 

(i) Mean

Production Yield

No. of farms

Mid value

A = 63.5

50 – 53

3

51.5

–12

–4

–12

53 – 56

8

54.5

–9

–3

–24

56 – 59

14

57.5

–6

–2

–28

59 – 62

30

60.5

–3

–1

–30

62 – 65

36

63.5

0

0

0

65 – 68

28

66.5

+3

+1

28

68 – 71

16

69.5

+6

+2

32

71 – 74

10

72.5

+9

+3

30

74 – 77

5

75.5

+12

+4

20

Total

 

 

 

 

= 63.5 + 0.32

= 63.82 kg per hectare

 

(ii) Median

 

Class Interval

Frequency

(f)

CF

50 – 53

3

3

53 – 56

8

11

56 – 59

14

25

59 – 62

30

55

62 – 65

36

91

65 – 68

28

119

68 – 71

16

135

71 – 74

10

145

74 – 77

5

150

Total

 

 

75th item lies in the 91st cumulative frequency and the corresponding class interval is 62 – 65.

 

 (iii) Mode

 

Grouping Table

 

 

 

Class Interval

I

II

III

IV

V

VI

 

 

 

 

 

 

 

 

 

50 – 53

3

 

 

 

 

 

 

11

22

25

52

 

53 – 56

8

   

 

 

 

 

 

 

56 – 59

14

 

 

 

 

 

 

44

 

 

 

59 – 62

30

   

 

 

 

 

 

 

62 – 65

 

 

 

 

 

 

44

 

54

 

65 – 68

28

   

 

 

 

 

 

 

68 – 71

16

 

 

 

 

 

 

26

15

31

 

 

 

71 – 74

10

   

 

 

 

 

 

 

74 – 77

5

 

 

 

 

 

 

               

 

  

                                                                                              Analysis Table

 

Column

50 – 53

53 – 56

56 – 59

59 – 62

62 – 65

65 – 68

68 – 71

71 – 74

74 – 77

I

 

 

 

 

 

 

 

 

II

 

 

 

 

 

 

 

III

 

 

 

 

 

 

 

IV

 

 

 

 

 

 

V

 

 

 

 

 

 

VI

 

 

 

 

 

 

Total

1

3

6

3

1

 

Modal class = 62 – 65

 

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