Question

Following is the frequency distribution of weight of seeds. Draw both the types of ogive curves and find the median

Weight (in mg)	11 - 20	21 - 30	31 - 40	41 - 50	51 - 60
No. of seeds	18	22	30	16	4

• A. Median $\approx$ 26
• B. Median $\approx$ 22
• C. Median $\approx$ 37
• D. Median $\approx$ 32.17

Answer 1

Answer: (C)

Median $\approx$ 37

$Weight\left(inmg\right)$	$No.ofseeds$
$10.5-20.5$	$18$
$20.5-30.5$	$22$
$30.5-40.5$	$30$
$40.5-50.5$	$16$
$50.5-60.5$	$4$

$\Rightarrow$ The ‘less than’ frequency table as shown below:

$Weight\left(inmg\right)$	$cf$
Less than $20.5$	$18$
Less than $30.5$	$18+22=40$
Less than $40.5$	$40+30=70$
Less than $50.5$	$70+16=86$
Less than $60.5$	$86+4=90$

$\Rightarrow$ The ‘more than’ frequency table as shown below:

$Weight\left(inmg\right)$	$cf$
More than $10.5$	$18+72=90$
More than $20.5$	$22+50=72$
More than $30.5$	$30+20=50$
More than $40.5$	$16+4=20$
More than $50.5$	$4$

$\Rightarrow$ The coordinates for less than curve are $(20.5,18),(30.5,40),(40.5,70),(50.5,86),(60.5,90)$

$\Rightarrow$ The coordinates for more than curve are $(10.5,90),(20.5,72),(30.5,50),(40.5,20),(50.5,4)$

The two curves intersect at point L. Draw $LM\perp OX$ cutting the x-axis at $M$. Clearly, $M=37$

Hence, $Median=37$