Question

ACT PREP QUESTION HELP: The median of a set f data containing 9 items was found. Four data items were added to the set. Two of these items were greater than the original median, and the other 2 items were less than the original median. Which of the following statements must be true about the median of the new data set????
-It is the average of the 2 new lower values
-it is the same as the original median
-it is the average of the 2 new higher values
-it is greater than the original median
-it is less than the original median

Answer 1

@Vocaloid

Answer 2

i would go with its the same as the original median since there wasnt any changes ..look at it this way... the median was found.. then four # was added 2 greater than median and 2 less than mean.. which gives 0.. so we still have the original median

Answer 3

yeah, it is B. I am practicing in a prep book and i know the answer but i just need to know how to do it

Answer 4

@LynFran

Answer 5

i think in my previous post ..thats all i have towards explaining this since they really wasnt specific with the value of the median...
ok lets see ...
let set ={1,2,3,4,5,6,7,8,9}
where n=9
then the median of such set is (n+1)/2 which gives (9+1)/2=5 meaning the 5th # in the set , so we locate the 5th # and that # is 5
now lets add 4 # (2 greater than the median, and 2 less than the median )
lets say (6 and 7) and (1 and 2) then \[\frac{ (6+7)-(1+2) }{ 2}=5\]... but it think it will be very carefully consider.. when choosing such value

Answer 6

lets test this using another set of data
let set ={2,4,6,8,10,12,14,16,18}
n=9
then (n+1)/2 ==> 9+1/2=5 the 5th place then median =10
now let choose 4 values (2<median , and 2> median)
lets say (15 and 20) and (7 and 8)
then \[\frac{ (15+20)-(7+8) }{ 2 }=10\]

Answer 7

It is important to know the definition of terms when solving these problems.
The median is defined as the "middle number", namely, with the same number of data greater than the median as less than.
For example, with nine values,

Answer 8

If we add two greater, and two smaller number than the median, it looks as follows:

We still have the same number of values less than as greater than the median.
So the median has not changed after the addition of 4 new values.