Question

Find the unknown entries $a,b,c,d,e$ and $f$ in the following distribution of heights of students in a class.

Height (in $cm$)	Frequency	Cumutative Frequcency
$150-155$	$12$	$a$
$155-160$	$b$	$25$
$160-165$	$10$	$c$
$165-170$	$d$	$43$
$170-175$	$e$	$48$
$175-180$	$2$	$f$
Total	$50$

Answer 1

Height ( in cm)	Frequency	Cumulative frequency given	Cumulative frequency
150-155	12	a	12
155-160	b	25	12+b
160-165	10	c	22+b
165-170	d	43	22+b+d
170-175	e	48	22+b+d+e
175-180	2	f	24+b+d+e
Total	50

On comparing last two tables, we get

$a=12$

$\therefore 12+b=25$

$\Rightarrow b=25-12=13$

$22+b=c$

$\Rightarrow c=22+13=35$

$22+b+d=43$

$\Rightarrow 22+13+d=43$

$\Rightarrow d=43-35=8$

$22+b+d+e=48$

$\Rightarrow 22+13+8+e=48$

$\Rightarrow e=48-43=5$

$24+b+d+e=f$

$\Rightarrow f=24+13+8+54=50$