 # What does the variance of a random variable measure? What is the standard deviation of a continuous random variable X? Tabansi 2020-10-21 Answered
What does the variance of a random variable measure?
What is the standard deviation of a continuous random variable X?
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Step 1
Variance of a random variable measures how far a set of (random) numbers are spread out from their average value.
Step 2
A continuous random variable is a random variable which takes infinitely many values. The continuous random variable can take any value between the ranges of values. Standard deviation of any variable is the mean distance of the random variable from the mean value. It determines the distribution of the data values around the mean. A smaller standard deviation indicates that the variable is distributed close to the mean value. A larger standard deviation indicates that the variable is distributed away from the mean value.
The formula for the standard deviation of the continuous random variable X is defined as:
$\sigma =\sqrt{{\int }_{-\propto }^{\propto }{\left(x-\mu \right)}^{2}f\left(x\right)dx}$