Question

4. (a) If the median of the data 7,3,10,5, x is the integer x then find x.
(b) If the numbers 25, 31, x - 3,37,x + 4, 42, 43, 45, 46 are in ascending order and their median is 39
then find x.
5. Find the median of the following data.
41, 43, 127, 99, 61, 92, 71,58,57
If 58 is replaced by 85 then find the new median.​

Answer 1

$\fontsize{18}{10}{\textup{\textbf{The new mean is 71}}}$

Step-by-step explanation:

(a) If x is the median, then the series becomes

3,5,x,7,10

SInce x is an integer, there is only one integer between 5 and 7, that is 6

So the required median is 6.

(b) Given series is in ascending order

25,31,x-3,37,x+4,42,43,45,46

Here x+4 is the middle term, so it is the median

given median=39

So x+4=39

=>x=35

5. Let us arrange the series in acsending order

41,43,57,58,61,71,92,99,127

There are 9 terms(odd)

So the middle term is the median

So median=61

Now replacing 58 by 85 and again arranging in ascending order

41,43,57,61,71,85,92,99,127

The series is changed and the new middle term is71

So, the new mean=71