Question

The following table gives the production yield per hectare of wheat of 100 farms of a village.

Production yield (kg/ha)	50−55	55−60	60−65	65−70	70−75	75−80
Number of farms	2	8	12	24	38	16

Change the distribution to a 'more than type' distribution and draw its ogive. Using ogive, find the median of the given data. [CBSE 2013]

Answer 1

The frequency distribution table of more than type is as follows:

Production yield (kg/ha) (lower class limits)	Cumulative frequency (cf)
More than 50	2 + 98 = 100
More than 55	8 + 90 = 98
More than 60	12 + 78 = 90
More than 65	24 + 54 = 78
More than 70	38 + 16 = 54
More than 75	16

Taking the lower class limits on x−axis and their respective cumulative frequencies on y−axis, its ogive can be obtained as follows:


Here, N = 100 $\Rightarrow \frac{N}{2}=50.$

Mark the point A whose ordinate is 50 and its x−coordinate is 70.5.


Thus, median of the data is 70.5.