Question

The monthly income (in rupees) of $7$ households in 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 Rs. $1500$ is added, what will the median income be?

• A. $i\left)1400ii\right)1450$
• B. $i\left)1450ii\right)1400$
• C. $i\left)1200ii\right)1450$
• D. $i\left)1000ii\right)1250$

Answer 1

The correct option is A $i\left)1400ii\right)1450$

$\left(i\right)$ Arranging house holds income in ascending order we get,

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

Number of house holds incomes $\left(n\right)=7$

$\Rightarrow$ $Median={\left(\frac{n+1}{2}\right)}^{th}householdincome={\left(\frac{7+1}{2}\right)}^{th}householdincome=4^{th}householdincome$

$\therefore$ $Median=1400$

$\left(ii\right)$ The order becomes after adding one more household monthly income $Rs.1500$

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

Number of house holds incomes $\left(n\right)=8$

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

$=\frac{1}{2}[4^{th}householdincome+5^{th}householdincome]$

$\therefore$ $Median=\frac{1400+1500}{2}=1450$