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 – 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

Answer 1

(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

75^th item lies in the 91^st 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