Find the median :
Weight No of students
$40 - 45$ $2$
$45 - 50$ $3$
$50 - 55$ $8$
$55 - 60$ $6$
$60 - 65$ $6$
$65 - 70$ $3$
$70 - 75$ $2$

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Solution

$W e i g h t$ $N o . o f s t u d e n t s$ $c . f .$
$40 - 45$ $2$ $2$
$45 - 50$ $3$ $5$
$50 - 55$ $8$ $13$
$55 - 60$ $6$ $19$
$60 - 65$ $6$ $25$
$65 - 70$ $3$ $28$
$70 - 75$ $2$ $30$
$N = 30$ and $\frac{N}{2} = \frac{30}{2} = 15$
$∴$ Median class $= 55 - 60$
$l = 55, c . f = 13, f = 6$ and $h = 5$
$M e d i a n = l + \frac{\frac{N}{2} - c . f}{f} \times h$

$= 55 + \frac{15 - 13}{6} \times 5$

$= 55 + 1.66$
$= 56.66$

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The distribution below gives the weights of $30$ students of a class. Find the median weight of the students.

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Weight	No of students
$40 - 45$	$2$
$45 - 50$	$3$
$50 - 55$	$8$
$55 - 60$	$6$
$60 - 65$	$6$
$65 - 70$	$3$
$70 - 75$	$2$

$W e i g h t$	$N o . o f s t u d e n t s$	$c . f .$
$40 - 45$	$2$	$2$
$45 - 50$	$3$	$5$
$50 - 55$	$8$	$13$
$55 - 60$	$6$	$19$
$60 - 65$	$6$	$25$
$65 - 70$	$3$	$28$
$70 - 75$	$2$	$30$

Find the median :WeightNo of students40−45245−50350−55855−60660−65665−70370−752

Weight No.ofstudents c.f. 40−45 2 2 45−50 3 5 50−55 8 13 55−60 6 19 60−65 6 25 65−70 3 28 70−75 2 30 N=30 and N2=302=15∴ Median class =55−60l=55,c.f=13,f=6 and h=5Median=l+N2−c.ff×h =55+15−136×5 =55+1.66 =56.66

Find the median :
Weight No of students
$40 - 45$ $2$
$45 - 50$ $3$
$50 - 55$ $8$
$55 - 60$ $6$
$60 - 65$ $6$
$65 - 70$ $3$
$70 - 75$ $2$