Question

Adding a constant 3 to any random variable will change the mean by a value of what?

Answer 1

The mean goes up by 3/5 where 3 is the amount of the constant that was added divided by the total number of numbers.

Explanation:

Let us suppose we have five number

`15,\:17,\:8,\:26,\:9`

Let us calculate the Mean of these numbers

`15,\:17,\:8,\:26,\:9`

The arithmetic mean is the sum of the values in the set divided by the number of elements in that set.

`\mathrm{Take\:the\:sum\:of\:}15,\:17,\:8,\:26,\:9`

`15+17+8+26+9=75`

`\mathrm{The\:number\:of\:terms\:in\:the\:data\:set\:is}=5`

`\mathrm{Divide\:the\:sum\:by\:the\:number\:of\:terms\:}=(75)/(5)`

Let us suppose we add constant 3 to the variable 8

`15+17+\left(8+3\right)+26+9\:`

`New\:mean\:=\:15+17+\left(8+3\right)+26+9\:=(78)/(5)`

so

New Mean - Old Mean:

`(78)/(5)-(75)/(5)=(3)/(5)`

The mean goes up by 3/5 where 3 is the amount of the constant that was added divided by the total number of numbers.