Question

Comparing the standard deviation and variance equation. Analyze the statement of "once is never; twice is forever"

Answer 1

Variance is a method to find or obtain the measure between the variables that how are they different from one another.
standard deviation shows us how the data set or the variables differ from the mean or the average value from the data set.

Variance helps to find the distribution of data in a population from a mean and standard deviation also helps to know the distribution of data in population
but standard deviation gives more clarity about the deviation of data from a mean.

Below are the formulas of variance and standard deviation.

variance formula

Whereas:
    σ2 is variance
    X is variable
    μ is mean
    N is the total number of variables.

Standard Deviation is the square root of the variance.

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The variance gives an approximate idea of data volatility. 68% of values are between +1 and -1 standard deviation from the mean.
That means Standard Deviation gives more details.
Variance measures the distribution of data in a population around the central value.
Standard deviation measures the distribution of data relative to the central value.

Sum of two variances (var(A + B ) ≥ var(A) + var(B ) .therefore variance is not coherent.
Sum of two standard Deviation sd(A + B ) ≤ sd(A) + sd(B ) so, Standard deviation is coherent.
It gives the idea of the skewness of the data. The value of skewness of symmetric distribution lies between -1>0>1.

he geometric mean is more sensitive to variance then Arithmetic mean.
A geometric standard deviation is used to find the bounds of the confidence interval in a population.