debbiem wrote:
set s contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70,94. It was found that Mark had inadvertently interchanged the digits of one of the numbers. Steve, in charge of statistics, rectified this error, and as a result mean and median were changed and the shift in mean was of 5.
Whats the number that was incorrectly noted?
A. 36
B. 49
C. 94
D. 27
E. 41
Firstly the NEW median will be 27 or 49...
secondly the change in SUM will be 9*5 = 45, so the difference in number and in reversed order will be 45...
and the reversed NUMBER and actual number should be on either side of the MEDIAN 36..
lets see the choices on these points..
A. 36... reverse = 63 but \(63-36\neq{45}\).... eliminate
B. 49... reverse = 94, and 94-49 = 45, BUT both 49 and 94 lie on the SAME side of 36, so no effect on MEDIAN... ELIMINATE
C. 94... SAME as B.. eliminate
D. 27.... reverse = 72.. 72-27 = 45.. yes and 27 is lesser than 36 and 72 is >36 so median will shift to 49... XORRECT
E. 41.... reverse 14, but \(41-14\neq{45}\).. eliminate
D