Question

Use the equation for variance below, along with the given data set, to answer the following questions. sigma squared = startfraction (x 1 minus mu) squared (x 2 minus mu) squared ellipsis (x n minus mu) squared over n endfraction what does the numerator evaluate to? what does the denominator evaluate to? the variance equals:

Answer 1

The given equation will be   $\sigma ^2=\dfrac{(x_1-\mu)^2+(x_2-\mu)^2+...........(x_n-\mu)^2}{N}$

What will be the value of variance?

From given data - sigma squared = start fraction (x 1 minus mu) squared (x 2 minus mu) squared ellipsis (x n minus mu) squared over n end fraction

The equation formed will be

$\sigma ^2=\dfrac{(x_1-\mu)^2+(x_2-\mu)^2+...........(x_n-\mu)^2}{N}$

What does the numerator evaluate-

The numerator contains the difference between the data and the mean which means that it shows how much the data is varied from its mean.

What does the denominator evaluate to?

The denominator represents the number of the given data. It is the total number of data given for the analysis.

The variance is the variation of each data from its mean.

Thus  The given equation will be  

$\sigma ^2=\dfrac{(x_1-\mu)^2+(x_2-\mu)^2+...........(x_n-\mu)^2}{N}$

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