Question 1181823
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Compute the mean by adding up the values, and dividing by n = 8, since there are 8 items in this list.


xbar = sample mean
xbar = (sum of values)/n
xbar = (15.2+18.8+19.3+19.7+20.2+21.8+22.1+29.4)/8
xbar = (166.5)/8
xbar = 20.8125


Then subtract the xbar value from each x value in the list. Square the difference. This forms the column (x-xbar)^2 as shown below<table border = "1" cellpadding = "5"><tr><td>x</td><td>(x-xbar)^2</td></tr><tr><td>15.2</td><td>31.50015625</td></tr><tr><td>18.8</td><td>4.05015625</td></tr><tr><td>19.3</td><td>2.28765625</td></tr><tr><td>19.7</td><td>1.23765625</td></tr><tr><td>20.2</td><td>0.37515625</td></tr><tr><td>21.8</td><td>0.97515625</td></tr><tr><td>22.1</td><td>1.65765625</td></tr><tr><td>29.4</td><td>73.74515625</td></tr></table>Adding up everything in that second column gives us 115.82875


Divide that by n-1 = 8-1 = 7
115.82875/7 = 16.5469642857142
This is the approximate value of the sample variance


Apply the square root to get
sqrt(16.5469642857142) = 4.06779599853708
This rounds to 4.07
The sample standard deviation is roughly 4.07


Answer: <font color=red>4.07 approximately</font>
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