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 households.
(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

Answer 1

Hint: : To find the median, it is first of all necessary to arrange the data in ascending order.
Then we have to determine the number of values in the given data set. If the number of values are odd then the middle value will be the median. If the number of values is even then we will have to take the average of the middle two values as the median for the given data set.

Complete step-by-step answer:
(i) The given incomes of 7 households are 1200, 1500, 1400, 1000, 1000, 1600 and 10000.
Thus, we will arrange them in ascending order as 1000, 1000, 1200, 1400, 1500, 1600 and 10000. Now, the number of incomes are 7 in number, which is an odd number, thus the median will be the middle value which, here will be the \[{4^{th}}\] value. Thus the median of the incomes of the 7 households will be Rs.1400.
(ii) Now, in the data set a new household is added with a monthly income of Rs.1500. Now, we will again arrange all the incomes, including the new one, in an ascending order.
Thus, the incomes arranged will be as 1000, 1000, 1200, 1400, 1500, 1500, 1600 and 10000.
Here, the number of values becomes an even number which is 8. So, to find the median, we will have to take the mean of the middle two values, which are \[{4^{th}}\] and \[{5^{th}}\] values.
The \[{4^{th}}\] and \[{5^{th}}\] value are 1400 and 1500 respectively, thus their mean will be given as \[\dfrac{{1400 + 1500}}{2}
= \dfrac{{2900}}{2}
= 1450
\].
Thus, the new median of the incomes of 8 households will be Rs.1450.
Hence, option (A) is the correct option.

Note: To find median, it is important to first of all arrange the given numbers in ascending order. Median does not indicate the average of the data set, however it is more or less close to the mean of the data, this is because if the frequency of a particular number is higher than the median will be closer to that number, thus closer to the mean.