Question

The frequency table displays the number of students of a class who spend varying amounts of time for doing their homework. Find the median of time spend doing their home work.

time (in sec)	$2$	$4$	$6$	$8$	$10$	$12$	$14$
frequency	$1$	$2$	$3$	$2$	$1$	$4$	$5$

• A. $10$
• B. $12$
• C. $11$
• D. $14$

Answer 1

Answer: (C)

$11$

$Time\left(insec\right)$	$Frequency$	$c.f$
$2$	$1$	$1$
$4$	$2$	$3$
$6$	$3$	$6$
$8$	$2$	$8$
$10$	$1$	$9$
$12$	$4$	$13$
$14$	$5$	$18$

$\Rightarrow$ $N=18$ (even)

$Median=\frac{1}{2}[{\left(\frac{18}{2}\right)}^{th}obs+{(\frac{18}{2}+1)}^{th}obs]$

$=\frac{1}{2}[9^{th}obs+{10}^{th}obs]$

Here, $9^{th}obs=10$ and ${11}^{th}obs=12$
$\therefore$ Required median $=\frac{1}{2}[10+12]$

$=11$