Your investment has a 9% chance of earning a 55% return, a 25% chance of earning an 17% rate of return, a 31% chance of earning an 9.25% rate of return, a 20% chance of losing 16%,and a 15% chance of losing 50%. What is the standard deviation of this investment?
probability 
return 
probability*return 

0.09 
55 
4.95 

0.25 
17 
4.25 

0.31 
9.25 
2.8675 

0.2 
16 
3.2 

0.15 
50 
7.5 

average return = sum of probability*return 
1.3675 

probability 
return 
returnaverage return 
square of (returnaverage return) 
probability*(square of returnaverage return) 
0.09 
55 
53.6325 
2876.445 
258.8801 
0.25 
17 
15.6325 
244.3751 
61.09376 
0.31 
9.25 
7.8825 
62.13381 
19.26148 
0.2 
16 
17.3675 
301.6301 
60.32601 
0.15 
50 
51.3675 
2638.62 
395.793 
average return = sum of probability*return 
1.3675 
Variance = sum of probability*(square of returnaverage return) 
795.3543 

standard deviation = square root of variance 
28.20 
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