Question

The following table gives production yield in kg. per hectare of wheat of 150 farms in a village. Calculate the 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

Mode 

Grouping Table

Class Interval	I	II	III	IV	V	VI
50 - 53	3
53 - 56	8	11	22	25	52	80
56 - 59	14
59 - 62	30	44	66		94
62 - 65	36
65 - 68	28	64	44		80	54
68 - 71	16
71 - 74	10	26	15	31
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

Mode = `L + (f_1 - f_0)/(2f_1 - f_0 - f_2) xx i`

= `62 + (36 - 30)/(2 xx 36 - 30 - 28) xx 3`

= `62 + 6/(72 - 30 - 28) xx 3`

= `62 + 6/14 xx 3`

= `62 + 18/14`

= 63.28 kg per hectare