**Definition**: Standard deviation is a measure of how far apart the data are from the average of the data. If all the observations are close to their average then the standard deviation will be small.

**How to calculate standard deviation:**

Suppose that an investor has $600 to invest and is considering investing all of it in the shares of one firm, currently trading at $30. The investor assesses a 0.75 probability that the shares will increase in market value to $33 over the coming period and a 0.25 probability that the share will decrease in its market value to $26. Assume that the firm will pay $1 dividend per share at the end of the year.

The payoffs from the proposed investment are as follows:-

If shares increase: $33 x 20 shares + $20dividend = $680

If shares decrease: $26 x 20 shares + $20dividend = $540

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680 | (680 - 600)/600 = 0.13 | 0.75 | 0.0975 | (0.13 - 0.0725)^2 x 0.75 = 0.0025 |

540 | (540 - 600)/600 = - 0.10 | 0.25 | -0.025 | (-0.1 - 0.0725)^2 x 0.25 = 0.0074 |

sum (x) | 0.0725 | Add the above two results to get σ² = 0.0099 |

The standard deviation is the square root of the variance. In the above example, the standard deviation is square root of 0.0099 i.e. 0.0995 or 9.95%

How to calculate the standard deviation using an ordinary calculator?

Key in 0.0099 and then press the √ key to get 0.0095 or 9.95%