Question

The monthly income (in rupees) of $7$ households in a village are $1200,1500,1400,1000,1000,1600,10000$.
(i) Find the median income of the house holds.
(ii) If one more household with monthly income of $1500$ is added, what will the median income be?

Answer 1

(i) Arrange income in ascending order

$1000$,$1000$,$1200$,$1400$,$1400$,$1500$,$1600$,$10000$

Here $n=7$

Median $={\left(\frac{n+1}{2}\right)}^{th}$

$={\left(\frac{7+1}{2}\right)}^{th}$

$=4^{th}$

$=1400$

(ii) If one more household with monthly salary $1500$ is added

then, arranging the income in ascending order

$1000$,$1000$,$1200$,$1400$,$1500$,$1500$,$1600$,$10000$

Here $n=8$

Meadian $=$ mean of ${\left(\frac{n}{2}\right)}^{th}$ and ${\left(\frac{n}{2}+1\right)}^{th}$ observations

$=$mean of ${\left(\frac{8}{2}\right)}^{th}$ and ${\left(\frac{8}{2}+1\right)}^{th}$ observation

$=$mean of ${\left(4\right)}^{th}$ and ${\left(5\right)}^{th}$ observations

$=$ $\frac{1400+1500}{2}$

$=1450$