Question

If you SCALE the data set ( multiply each element by 4 ) , what will happen to the mean ,median , mode . prove it mathematically by using equations .

please show ALL steps.

Answer 1

Since the mean is calculated as

lets take an example as

Now if we multiply each value with 4 then the mean will also beome 4 time the original value hence if multiplied by 5 the mean is also gets multiplied by 4.

b) Since the median does not commute value with it and it is actually the middle value of the data ser hence if we multiply 4 to the median the median willl also become 4 times the earlier value.

c) Simillarly the mode is also the value which appers most of the time in a data set hence if we multiply 4 to al the dta the mode will also multipiled by 4 hence producing a 4 time Mode.