Question

Six years ago, you purchased 100 shares of lit stock. the annual returns have been 14 percent, 9 percent, 16 percent, 24 percent, - 40 percent, and 4 percent, respectively for those six years. what is the standard deviation of these returns?

Answer 1

20.83%
The basic definition of the standard deviation is the square root of the mean of the squares of the difference from the mean. So let's first calculate the mean:
(14+9+16+24-40+4)/6 = 27/6 = 4.5
Now the mean of the squares of the difference from the mean:
((14-4.5)^2+(9-4.5)^2+(16-4.5)^2+(24-4.5)^2+(-40-4.5)^2+(4-4.5)^2)/6
= (9.5^2+4.5^2+11.5^2+19.5^2+(-44.5)^2+(-0.5)^2)/6
= (90.25 + 20.25 + 132.25 + 380.25 + 1980.25 + 0.25)/6
= 2603.5/6
= 433.9166667
And finally, the square root. So
sqrt(433.9166667) = 20.8306665
So the standard deviation of those returns is 20.83%