Question

13. Measures of variability match-up

There are multiple ways to refer to or describe a variance or a standard deviation of either a population or a sample. Likewise, each measure has multiple appropriate equations or symbols. The first table consists of alternative ways of referring to each of these measures. The second table consists of equations or symbols for each of these measures.

Alternative Description

	a. Average squared distance from M
	b. Square root of the average squared distance from μ
	c. Average squared distance from μ
	d. Square root of the average squared distance from M

Equation or Symbol

1.	SS / (n – 1)
2.	∑(X – μ)² / N
3.	√(∑(X – μ)² / N)
4.	√(SS / (n – 1))

For each of the following four measures, select one appropriate description from the first table (lettered) and one appropriate equation or symbol from the second table (numbered). Each answer will be used only once.

Measure	Alternative Description	Equation or Symbol
Population standard deviation
Population variance
Sample standard deviation
Sample variance

Answer 1

Measure	Alternative Description	Equation or Symbol
Population standard deviation	b. Square root of the average squared distance from μ	3. √(∑(X – μ)² / N)
Population variance	c. Average squared distance from μ	2. ∑(X – μ)² / N
Sample standard deviation	d. Square root of the average squared distance from M	4. √(SS / (n – 1))
Sample variance	a. Average squared distance from M	1. SS / (n – 1)