Question

The daily wages of $80$ workers in a project are given.
Use a graph paper to draw an ogive for the above distribution.(Use of scale of $2\text{cm}=\text{Rs.}50$ on $x$-axis and $2\text{cm}=10$ workers on $y$-axis). Use your ogive to estimate.

Wages (in $\text{Rs.}$)	$400-450$	$450-500$	$500-550$	$550-600$	$600-650$	$650-700$	$700-750$
No. of workers	$2$	$6$	$12$	$18$	$24$	$13$	$5$

$1.$ The median wage of the workers.
$2.$ The lower quartile wage of workers.
$3.$ The number of workers who earn more than $\text{Rs.}625$ daily.

Answer 1

Upper class boundary	Cummulative frequency	Lower class boundary	Cummulative frequency
$400$	$0$	$400$	$80$
$450$	$2$	$450$	$78$
$500$	$8$	$500$	$72$
$550$	$20$	$550$	$60$
$600$	$38$	$600$	$42$
$650$	$62$	$650$	$18$
$700$	$75$	$700$	$5$
$750$	$80$	$750$	$0$

$1).$ Median can be found by intersection of upper class and lower class boundary ogive or drawing perpendicular to half of cummulative frequency median is equal to $Rs.\mathrm{603.75.}$
$2).$ Lower quartile wage of workers can be found by dividing cummulative frequency in four parts that is $\frac{80}{4}=20$ so, corresponding to $20$ in upper class boundary we get $Rs.550$ that is lower quartile.

$3).$ And the number of workers who earn more than $Rs.625$ can be found from lower-class boundary ogive that is $30$ workers.