Question 1190485
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First we add up all the values
(-5)+(3)+(-5)+(-5)+(-3)+(-3)+(-3) = -21


Then divide by n = 7 because there are 7 items in this list
-21/n = -21/7 = -3


The sample mean is xbar = -3


Next, we subtract xbar from each item
-5 - xbar = -5 - (-3) = -2
3 - xbar = 3 - (-3) = 6
-5 - xbar = -5 - (-3) = -2
-5 - xbar = -5 - (-3) = -2
-3 - xbar = -3 - (-3) = 0
-3 - xbar = -3 - (-3) = 0
-3 - xbar = -3 - (-3) = 0


Perhaps it's better to use a table to organize the data values<table border = "1" cellpadding = "5"><tr><td>x</td><td>x-xbar</td></tr><tr><td>-5</td><td>-2</td></tr><tr><td>3</td><td>6</td></tr><tr><td>-5</td><td>-2</td></tr><tr><td>-5</td><td>-2</td></tr><tr><td>-3</td><td>0</td></tr><tr><td>-3</td><td>0</td></tr><tr><td>-3</td><td>0</td></tr></table>


The next step is to square each item in the second column to form the column (x-xbar)^2<table border = "1" cellpadding = "5"><tr><td>x</td><td>x-xbar</td><td>(x-xbar)^2</td></tr><tr><td>-5</td><td>-2</td><td>4</td></tr><tr><td>3</td><td>6</td><td>36</td></tr><tr><td>-5</td><td>-2</td><td>4</td></tr><tr><td>-5</td><td>-2</td><td>4</td></tr><tr><td>-3</td><td>0</td><td>0</td></tr><tr><td>-3</td><td>0</td><td>0</td></tr><tr><td>-3</td><td>0</td><td>0</td></tr></table>


Add up everything in the third column:
4+36+4+4+0+0+0 = 48


Then divide by n-1 = 7-1 = 6 to compute the sample variance
48/(n-1) = 48/6 = 8


Such a process is fairly tedious busywork if you are dealing with large data sets. 
I recommend using a calculator such as this one
<a href = "https://www.calculatorsoup.com/calculators/statistics/variance-calculator.php">https://www.calculatorsoup.com/calculators/statistics/variance-calculator.php</a>
and this is a handy tool to check your work.


To compute the standard deviation, you apply the square root to the variance
Standard Deviation = sqrt(variance)



Answer: <font color=red>8</font>
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