14 Identify weather the following variables are numerical or

14. Identify weather the following variables are numerical or categorical. If numerical, state whether the variable is discrete or continuous. If categorical, state whether the categories have a natural order (ordinal) or not (nominal).

a) Number of sexual partners in a year... b) petal area of rose flowers... c) heartbeats per minut of a Tour de France cyclist, averaged over the duration of the race... d) birth weight... e) stage of fruit ripeness (underripe, ripe, or overripe)... f) angle of flower otrientation relative to postion of the sun ... g) tree species... h) year of birth... i) gender

22. Researchers sent out a survey to U.S. war veterans that asked a series of questions, including whether individuals surveyed were smokers or nonsmokers. They found that nonsmokers were 27% more likely than smokers to respond to a survey within 30 days (based on the much larger number of smokers and nonsmokers who eventually responded). Hypothetically, if the study had ended after 30 days, what effect would this have on the estimate of the proportion of veterans who smoke?

31. In Poland students are required to achieve a score of 21 or higher on the high-school Polish language “maturity exam” to be eligible for university. The following graph shows the frequency distribution of scores.

a) Examine the graph and identify the most conspicuous pattern in these data.

b) Generate a hypothesis to explain the pattern.

Solution

14.

a) Number of sexual partners in a year...

NUMERICAL. Discrete, as you cannot half fraction of a sexual partners, like 8.5 sexual partners.

b) petal area of rose flowers...

NUMERICAL. Continuous, as they can take any area greater than 0.

c) heartbeats per minut of a Tour de France cyclist, averaged over the duration of the race...

NUMERICAL. Continuous, as it is averaged so it can take decimal values.

d) birth weight...

NUMERICAL. Continuous, as it can take any value greater than 0.

e) stage of fruit ripeness (underripe, ripe, or overripe)...

CATEGORICAL. It is ordinal, as it follows a certain order.

f) angle of flower otrientation relative to postion of the sun ...

NUMERICAL. Continuous, as it can take any value of an angle.

g) tree species...

CATEGORICAL. Nominal, as there is no natural ordering.

h) year of birth...

CATEGORICAL. Ordinal, as it has a certain order.

i) gender

CATEGORICAL. Nominal, as there is no natural ordering.

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