The following table gives production yield in kg per hectare of wheat of 150 farms in a village - Economics - Measures of Central Tendency

Question

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 â€“ 53

53 â€“ 56

56 â€“ 59

59 â€“ 62

62 â€“ 65

65 â€“ 68

68 â€“ 71

71 â€“ 74

74 â€“ 77

Number of farms

3

8

14

30

36

28

16

10

5

Bhawna Madaan · Accepted Answer

(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

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

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

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

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

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	–	–