what will happen to the mean, median, mode, range, and Standard Deviation if...?

Question

1. you add a positive number X to every element of the data set?
2. you multiply every element of the data set by a positive number X?

explain and if possible give an example (second part is optional but would help a lot)~

Answer 1

Simple example:



The numbers are 3,4,4,5; 4 cases



mean = 4

median = 4

mode= 4



Add a constant 3 to each observation.

6,7,7,8

Mean = 7

Median = 7

Mode = 7

They are all 3 more than what they were.



The standard deviation will not change if you add a constant. You can verify this yourself.



Multiplying:

Let us multiply each observation by 2.

3,4,4,5

6,8,8,10

after multiplication:

Mean =8

Median = 8

Mode = 8

The mean, median, and mode are also multiplied by 2.



The standard deviation will also be multiplied by 2.

Verify this yourself.

Answer 2

1. The mean, median and mode would also increase by X.

The range will not change. The standard deviation will change indefinitely.



2. the mean, median and mode will also become X times larger than the original values. the range will be X times the largest data.

Answer 3

what will happen:

1. mean > mean+X

median > median+X

mode > mode+X

range > nothing (same range)

Standard Deviation > nothing (same)









2. mean > mean*X

median > median*X

mode > mode*X

range > range*X

Standard Deviation > |x|*Standard Deviation