Question

An unknown distribution has a mean of $100$, a standard deviation of $100$, and a sample size of $100$. Let $X=$one object of interest.

What is the standard deviation of $\Sigma X$?

Short answer

The standard deviation of$\sum X$is$1000$.

Step-by-step solution

Given Information

According to the provided details, the mean of the unknown distribution is $100$, the standard deviation is $100$and the sample size is $100$objects of interest.

Explanation

The standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Mean is the mathematical average of a set of two or more numbers.

Thus the standard deviation of $\sum x$is given as:

$=\left(\sqrt{n}\right)\left({\sigma }_X\right)$

$=\sqrt{100}\times 100$

$=1000$