Question

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

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	∑f = 150

Median class = Size of `(N/2)^{th}` item

= Size of `(150/2)^{th}` item = 75^th item

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

Median = `L + (N/2 - CF)/f xx i`

= `62 + (75 - 55)/36 xx 3`

= `62 + 20/36 xx 3`

= 63.67 kg per hectare