Discussion: Getting Started

It is very important to understand the difference between quantitative and qualitative variables because

certain calculations can only be performed on quantitative variables such as correlation and regression.

Qualitative variables place items into categories or labels, such as red cars in a garage. The level of

measurement can be nominal if there is no ranking, such as small, medium, and large. If the items can be

ranked, the level of measurement is ordinal. Qualitative variables are neither discrete nor continuous.

Quantitative variables result from counts or measurements, such as a child’s height in inches. The level of

measurement can be interval if intervals are meaningful, but ratios are not. Data at this level will have an

arbitrary zero point. The ratio level of measurement will have meaningful intervals and a true zero starting

point. Quantitative variables can be discrete or continuous. If a data value can take on a decimal value, it is

continuous. If a data value can take on only whole number values, it is discrete.

In determining the level of measurement of a variable, start by determining if the variable is qualitative or

quantitative. If the variable is qualitative, the level of measurement can only be nominal or ordinal. If the

variable can be put in some type of order, such as good, better, best, it is ordinal. If there is no order to the

variable, such as color of a car, it is nominal. If the variable is quantitative, it can only be interval or ratio. If

the variable can have a value of 0 that means the variable has none of the quantity present, it is ratio, such as

the length of a car. If the variable does not have a zero that represents no quantity, such as outdoor

temperature, it is interval.

Watch the following video: http://www.youtube.com/watch?v=B0ABvLa_u88

Example: Label the following variables as either discrete or continuous.

a. The number of eggs that a hen lays in a week

b. The amount of milk that a cow produces in a month.

c. The word count from a page of a novel.

d. The amount of liquid detergent used in a washing machine in a month.

e. The number of baskets made by a team in a tournament.

f. Red cars in a parking garage.

Solution: a. Since we are counting the number of eggs and it is a whole number, this is discrete.

b. We are measuring the amount of milk which can take on decimal values, so this is continuous.

c. We are counting the number of words, so this is discrete.

d. Since this is a measurement, it is continuous.

e. Since this is a count of baskets, it is discrete.

f. Since this is a qualitative variable, it is neither discrete nor continuous.

Example: Label the following variables as quantitative or qualitative.

a. The age in years of respondents to a survey.

b. The political party affiliation of respondents to a survey.

c. Colors of M&M candies

d. The cubic centimeters in the engine of a SUV.

Solution: a. The age is an objective, measurement of how long someone has lived so it is quantitative.

b. The political party affiliation would be Democrat, Republican, Independent, etc. so it is a label and

qualitative.

c. The colors of M&M’s is red, yellow, brown, etc. so this is a label and qualitative.

d. The number of cubic centimeters in an engine is an objective, numerical measurement of the size of an

engine so it is quantitative.

Example: Find the level of measurement of the following variable?

a. Depth (ft) tremors felt from an earthquake

b. Flight numbers of 48 different flights

c. Ranking of colleges by INC magazine

d. The blood lead level measured as low, medium, or high e. SAT score

Solution: a. the depth of tremors is a quantitative variable (a measurement) so it is interval or ratio. Since a

depth of 0 means no tremors, this is ratio level.

b. The flight number is a qualitative variable and since the number can’t be ranked with any meaning, this is

nominal.

c. The ranking of colleges is qualitative, and the ranking can be ordered in a good, better, best type of ranking

so this is ordinal.

d. The blood lead level is quantitative because it is a measurement and can have a true value of 0 meaning

you have no lead in your blood, so this is ratio.

e. A SAT score is a measurement of knowledge, so it is quantitative. If you participate in taking the test, you

will not make a 0 so there isn’t a true 0, and this is interval level.