Q 110. - The Practice of Statistics for AP

Question

What are all the values that a standard deviation $s_x$ can possibly take?

(a)$s_x \ge 0$

(b)$s_x > 0$

(c) $0 \le s_x \le 1$

(d) $-1 \le s_x \le 1$

(e) Any number 

Step-by-Step Solution

Answer

The correct option is (a)$s_x\ge 0$

Step 1: The given information

All the values that a standard deviation $s_x$can possibly take will be calculated. Standard deviation is a measurement that is used to spread out mean data.

Step 2: Explanation

$s_x=0$ means that $s_x$is always higher than or equal to $0$ If all of the observations have the same value and no variability, then  $s_x>0$, this indicates that the observations are dispersed about the mean.

As a result, the proper option is  $s_x\ge 0$.

Step 3: Concept

Statistical Measures are a descriptive-analytical technique that provides an overview of a data set's properties.