The following table gives production yield per hectare of Wheat of $100$ farmers of a village.
Production yield
(Quintal/Hec) $50 - 55$ $55 - 60$ $60 - 65$ $65 - 70$ $70 - 75$ $75 - 80$
Number of
farmers $2$ $24$ $16$ $8$ $38$ $12$
Draw both Ogives for the above data. Hence obtain the median production yield.

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Solution

Production yield (Quintal/hee) Frequency (No. of farmers) Increasing Cumulative Average Decreasing Cumulative Average
$50 - 55$ $2$ $2$ $100$
$55 - 60$ $24$ $26$ $98$
$60 - 65$ $16$ $42$ $74$
$65 - 70$ $8$ $50$ $58$
$70 - 75$ $38$ $88$ $50$
$75 - 80$ $12$ $100$ $12$
$∴$ So, from the graph, where two Ogives intersect.
We get the median and it is $68.75$ .

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Number of farms	$2$	$8$	$12$	$24$	$38$	$16$

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Production yield (Quintal/Hec)	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$
Number of farmers	$2$	$24$	$16$	$8$	$38$	$12$

Production yield (Quintal/hee)	Frequency (No. of farmers)	Increasing Cumulative Average	Decreasing Cumulative Average
$50 - 55$	$2$	$2$	$100$
$55 - 60$	$24$	$26$	$98$
$60 - 65$	$16$	$42$	$74$
$65 - 70$	$8$	$50$	$58$
$70 - 75$	$38$	$88$	$50$
$75 - 80$	$12$	$100$	$12$

The following table gives production yield per hectare of Wheat of 100 farmers of a village.Production yield(Quintal/Hec)50−5555−6060−6565−7070−7575−80Number of farmers2241683812Draw both Ogives for the above data. Hence obtain the median production yield.