Question 1190757
<font color=black size=3>
n = 10 = sample size


Add up the numbers and you should get 1530
Divide that over the n = 10 numbers. This yields the sample mean of 1530/10 = 153


xbar = 153 = sample mean


Next, subtract the sample mean from each item. 
I recommend making a table to organize the data.<table border = "1" cellpadding = "5"><tr><td>x</td><td>x-xbar</td></tr><tr><td>164</td><td>11</td></tr><tr><td>165</td><td>12</td></tr><tr><td>157</td><td>4</td></tr><tr><td>164</td><td>11</td></tr><tr><td>152</td><td>-1</td></tr><tr><td>147</td><td>-6</td></tr><tr><td>148</td><td>-5</td></tr><tr><td>131</td><td>-22</td></tr><tr><td>147</td><td>-6</td></tr><tr><td>155</td><td>2</td></tr></table>The second column tells us the error of each x value with respect to the center xbar = 153.


Square each item in the second column to form the third column.<table border = "1" cellpadding = "5"><tr><td>x</td><td>x-xbar</td><td>(x-xbar)^2</td></tr><tr><td>164</td><td>11</td><td>121</td></tr><tr><td>165</td><td>12</td><td>144</td></tr><tr><td>157</td><td>4</td><td>16</td></tr><tr><td>164</td><td>11</td><td>121</td></tr><tr><td>152</td><td>-1</td><td>1</td></tr><tr><td>147</td><td>-6</td><td>36</td></tr><tr><td>148</td><td>-5</td><td>25</td></tr><tr><td>131</td><td>-22</td><td>484</td></tr><tr><td>147</td><td>-6</td><td>36</td></tr><tr><td>155</td><td>2</td><td>4</td></tr></table>


Add up everything in the third column to get 988. This is the sum of the squared errors (SSE). As the name implies, it's the result of adding up each error squared. Each x-xbar value is the error itself, and we square the item to avoid a negative number. This means any (x-xbar)^2 has a min value of 0.


Divide this SSE value over n-1 = 10-1 = 9 to compute the sample variance.
SSE/(n-1) = 988/9 = 109.7778 approximately


Apply the square root to the sample variance to get the sample standard deviation
sqrt(988/9) = 10.4775 approximately


You can use a graphing calculator to check the answers. 
Or you can use a free dedicated online 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>
Make sure the "sample" option is selected.


-----------------------


In summary:
sample variance = 109.7778
sample standard deviation = 10.4775 
both values are approximate
</font>