# What is the avg return (arithmetic)?, geometic avg return?, variance? standard deviation? Y/R: 1/ 0.15,2/ 0.03, 3 -0.25, 4/ 0.07,5/ 0.16

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### 1 Answer

The average return is

`sum_1^n (x_i/n) = bar(x) = (0.15+0.03-0.25+0.07+0.16)/5 = 0.16/5 = 0.032`

The geometric average of the returns is

`root(n)(x_1x_2...x_n) = root(5)((0.15)(0.03)(-0.25)(0.07)(0.16)) = root(5)(-1.26"e"^(-5)) `

`= -0.105`

The variance of the returns is

`sum_1^n(x_i-bar(x))^2/n = sum_1^n(x_i^2/n) -bar(x)^2`

`= (0.15^2+0.03^2+0.25^2+0.07^2+0.16^2)/5 -0.032^2 = 0.1164/5-0.032^2 = 0.022`

The standard deviation of the returns is the square root of the variance of the returns = `sqrt(0.022) = 0.149`

**Arithmetic mean 0.032**

**Geoemtric mean -0.105**

**Variance 0.022**

**Standard deviation 0.149**