Question

# The monthly income (in rupees) of $$7$$ households in village are $$1200, 1500, 1400, 1000, 1000, 1600, 10000.$$Â (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)1400 ii)1450
B
i)1450 ii)1400
C
i)1200 ii)1450
D
i)1000 ii)1250

Solution

## The correct option is A $$i)1400\ ii)1450$$$$(i)$$  Arranging house holds income in ascending order we get,$$1000,1000,1200,1400,1500,1600,10000$$Number of house holds incomes $$(n)=7$$$$\Rightarrow$$  $$Median=\left(\dfrac{n+1}{2}\right)^{th}house hold\,income=\left(\dfrac{7+1}{2}\right)^{th}household\,income=4^{th}household\,income$$$$\therefore$$  $$Median=1400$$$$(ii)$$  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 $$(n)=8$$$$\Rightarrow$$  $$Median=\dfrac{1}{2}\left[\left(\dfrac{n}{2}\right)^{th}house hold\,income+\left(\dfrac{n}{2}+1\right)^{th}household\,income\right]$$                      $$=\dfrac{1}{2}\left[4^{th}household\,income+5^{th}household\,income\right]$$$$\therefore$$  $$Median=\dfrac{1400+1500}{2}=1450$$Mathematics

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