Do you remember the previous mountain entry that detailed how to calculate the standard deviation in the case of only $2$ numbers? If not, go review that. Okay, now that you know, we can easily demonstrate What Happens to Standard Deviation when...

We Add or Subtract the Same Number to Each Number

Imagine our dataset consists of only two numbers, $6$ and $8$, with a standard deviation of $1$. Let's add the number $4$ to both numbers.

$$6+4, 8+4$$

$$10,12$$

The standard deviation is still $1$. So what happens when we add (or subtract) something to every number? NO CHANGE.

We Multiply or Divide Each Number by the Same Number

Starting with our simple dataset of two numbers, $6$ and $8$, with a standard deviation of $1$, let's multiply each number by $3$.

$$6 \times 3, 8 \times 3$$

$$18, 24$$

The standard deviation is now $3$. So what happenes when we multiply (or divide) each number by something? CHANGE (by a factor of what we're multiplying or dividing by).

NOTE 1: If every number in a dataset is the same, the standard deviation is $0$. Multiplying or dividing each number by another number will still result in a standard deviation of $0$.

NOTE 2: Multiplying every number in a dataset by $-2$ for example increases the standard deviation by a factor of $2$, not $-2$.