Variance and standard deviation

Post by **amh** » Fri Dec 22, 2023 11:02 am

1. What is variance?

The average of squared differences between data point and the mean

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2. What does it tell?

It exhibits how the data point vary with according to mean and provides an insight to variability of the data points

3. Value interpretation

Lower value of variance indicates many of data points values are close to the mean, while large variance tells the opposite.

4. Variance formula

$\sigma^2(sample) = \frac{\sum (x_i - \overline {x})^2}{n-1}$

$x_i = data point$

$\overline {x} = mean\:of\:sample$

$n= number\:of\:data$

$\sigma^2(population) = \frac{\sum (x_i - \overline {x})^2}{n}$

$x_i = data point$

$\overline {x} = mean\:of\:population$

$n= number\:of\:data$

5. Example of variance applications ?

Statistical formulas, finance

Post by **amh** » Thu Dec 28, 2023 6:55 am

1. What is standard deviation?

A measure of typical data dispersion from mean / average difference of data from mean value

2. What is the relationship between variance and standard deviation?

$Standard\:Deviation(SD) = \sqrt{Variance}$

The Equation:

$\sigma = \sqrt\frac{\sum (x_i - \overline {x})^2}{n}$

$x_i = data point$

$\overline {x} = mean\:of\:data$

$n= number\:of\:data$