<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-what-happens-to-sd-when" target="_blank">What happens to SD when... Exercise</a></p><p>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 <strong><span style="color:#8e44ad;">What Happens to Standard Deviation</span></strong> when...</p>
<p><strong><span style="color:#2980b9;">We Add or Subtract the Same Number to Each Number</span></strong></p>
<p style="margin-left: 40px;">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.</p>
<p>$$6+4, 8+4$$</p>
<p>$$10,12$$</p>
<p style="margin-left: 40px;">The standard deviation is still $1$. So what happens when we add (or subtract) something to every number? <strong><span style="color:#e74c3c;">NO CHANGE</span></strong>.</p>
<p><strong><span style="color:#2980b9;">We Multiply or Divide Each Number by the Same Number</span></strong></p>
<p style="margin-left: 40px;">Starting with our simple dataset of two numbers, $6$ and $8$, with a standard deviation of $1$, let's multiply each number by $3$.</p>
<p>$$6 \times 3, 8 \times 3$$</p>
<p>$$18, 24$$</p>
<p style="margin-left: 40px;">The standard deviation is now $3$. So what happenes when we multiply (or divide) each number by something? <strong><span style="color:#27ae60;">CHANGE</span></strong> (by a factor of what we're multiplying or dividing by).</p>
<p><strong><u>NOTE 1</u></strong>: 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 $0$.</p>
<p><strong><u>NOTE 2</u></strong>: Multiplying every number in a dataset by $-2$ for example increases the standard deviation by a factor of $2$, not $-2$.</p>