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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)1400 ii)1450
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B
i)1450 ii)1400
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C
i)1200 ii)1450
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D
i)1000 ii)1250
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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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