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?

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%