Standard Deviation and Variance

Standard Deviation and Variance

\[Population{\text{ }}Variance{\text{ }}\sigma 2{\text{ }} = {\text{ }}\frac{{\left( {\sum {{{\left( {{X_i} - \mu } \right)}^2}} } \right)}}{N}\]

\[Standard{\text{ }}Deviation{\text{ }}\sigma {\text{ }} = {\text{ }}\sqrt {Variance} \]

\[Sample{\text{ }}Variance{\text{ }}{\sigma ^2}{\text{ }} = \frac{{\left( {\sum {{{\left( {{X_i} - \mu } \right)}^2}} } \right)}}{{N - 1}}\]

Where:

• σ is the Standard deviation
• σp is the Standard deviation of portfolio return
• s is the Sample standard deviation
• n is the Size of the sample
• σx is the Standard error of sample mean
• x is the Point estimate of population mean

Instructions to use calculator

1. Enter the scientific value in exponent format, for example if you have value as 0.0000012 you can enter this as 1.2e-6
2. Please use the mathematical deterministic number in field to perform the calculation for example if you entered x greater than 1 in the equation \[y=\sqrt{1-x}\] the calculator will not work and you may not get desired result.
3. Pay attention to the (*) field,this is the field which can not explicitly expressed from other variable and should be calculated Iteratively, i.e in the first iteration you should enter dummy value in this field along with the other fields value and run the calculation, in the next iteration adjust the value of other fields to get the desired result for example in the sum of n term of GP equation \[{{S}_{n}}=a\left( \frac{1-{{r}^{n}}}{1-r} \right)\] to calculate r (which cannot be expressed explicitly in terms of a,n) enter some arbitrary value of r in the first iteration along with the values of a and n and in the next iteration adjust the value of a and n to get correct value of r
4. You should reset calculator for new calculation however result of last field can be recalculated without reset the calculator, you just need to change the value of other fields.
5. If you find something wrong please report us through report icon or write us through contact us