Question

What is the variance sign?

Answer 1

Hint: In order to answer the question given, we must have a brief information or knowledge regarding the variance. The sign of variance is nothing but the variable or the symbol which is used to denote the variance.

Complete step-by-step solution:
Now let us learn more about variance. Variance is nothing but the difference between the data points from the mean or simply we can say that how far the data is spread out from the mean. In the same way, if the variance value is low it means that measures of dispersion is less. If the value of the variance is high, we must know that the data is scattered at a larger distance from the mean. The formula for finding the variance of a data is \[Var\left( x \right)=E\left[ {{\left( X-\mu \right)}^{2}} \right]\]. We can simply say that the square of standard deviation is equal to the variance.
Now let us denote the sign of the variance.
The symbol or the sign of the variance is \[{{\sigma }^{2}},{{S}^{2}}\] or \[Var\left( X \right)\].
Let us consider an example and find the variance of the given observation.
Find the population variance of the data given.

MEASURE	VALUE
\[\mu \]	50
\[\sigma \]	4

Now let us find the variance.
\[{{\sigma }^{2}}={{4}^{2}}=16\]
Hence the population variance is \[16\].

Note: Variance considers all the dispersions from the mean either positive or negative. So we can have both positive and negative values for variance. While solving for variance, the main advantage is that it gives combined weight to the extreme values but while finding the variance of a data, the calculation might become complicated.