Question

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

Height (in $\mathrm{cm}$)	Frequency	Cumulative Frequency given
$150-155$	$12$	$a$
$155-160$	$b$	$25$
$160-165$	$10$	$c$
$165-170$	$d$	$43$
$170-175$	$e$	$48$
$175-180$	$2$	$f$
Total	$50$

Answer 1

Step 1: Generating expressions for the variables

Height (in $\mathrm{cm}$)	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	$50$

Step 2: Comparing the last two columns

On comparing the last two columns of the table, we obtain,

$$\begin{gathered} a=12 \\ \therefore 12+b=25 \\ \Rightarrow b=13 \\ 22+b=c \\ \Rightarrow c=22+13=35 \\ 43=22+b+d \\ \Rightarrow d=43-22-13=8 \\ 48=22+b+d+e \\ \Rightarrow e=48-22-13-8=5 \\ f=24+b+d+e \\ \Rightarrow f=24+13+8+5=50 \end{gathered}$$

Therefore, the values are, $a=12$, $b=13$, $c=35$, $d=8$, $e=5$ and $f=50$