Variables, Measurement, and Data Types: 10 practice questions

Question 1 of 10

A customer ID is stored as six digits. What determines whether it is categorical or quantitative?

1. AA measured amount becomes categorical whenever analysts group it for a chart, and the discarded within-group magnitudes remain fully recoverable.
2. BCategorical variables represent groups or labels, while quantitative variables have numerical magnitudes for which arithmetic comparisons are meaningful.
3. CA discrete variable can take every value in an interval, while a continuous variable must have a finite list of possible values.
4. DAny variable stored as digits is quantitative, so arithmetic on account codes or postal codes has an interpretable magnitude and average.

Question 2 of 10

A satisfaction scale runs from dissatisfied to very satisfied. Why is it ordinal rather than nominal or interval-scaled?

1. AA measured amount becomes categorical whenever analysts group it for a chart, and the discarded within-group magnitudes remain fully recoverable.
2. BNominal categories have no intrinsic order, whereas ordinal categories have an order without guaranteed equal spacing between levels.
3. CAny variable stored as digits is quantitative, so arithmetic on account codes or postal codes has an interpretable magnitude and average.
4. DA variable is continuous only if the observed sample contains infinitely many distinct recorded values.

Question 3 of 10

Which distinction separates a purchase count from an underlying transaction time?

1. AThe observational unit is whichever column has the most unique values.
2. BA variable is continuous only if the observed sample contains infinitely many distinct recorded values.
3. CA discrete quantitative variable has a finite or countable set of possible values, while a continuous variable can take values across an interval.
4. DA discrete variable can take every value in an interval, while a continuous variable must have a finite list of possible values.

Question 4 of 10

Why can a numeric-looking postal code not be treated like a measured magnitude?

1. AA column stored as numbers can still be categorical when the numbers are identifiers or codes rather than measured magnitudes.
2. BA variable is continuous only if the observed sample contains infinitely many distinct recorded values.
3. COne row always represents one independent person, even when the table contains transactions, visits, or repeated measurements from the same person.
4. DA discrete variable can take every value in an interval, while a continuous variable must have a finite list of possible values.

Question 5 of 10

What does defining one row as one customer establish before classifying the columns?

1. AOne row always represents one independent person, even when the table contains transactions, visits, or repeated measurements from the same person.
2. BThe observational unit determines what one row represents, and each measured characteristic becomes a variable for that unit.
3. CMeans and standard deviations are the natural summaries for unordered category labels.
4. DThe observational unit is whichever column has the most unique values.

Question 6 of 10

A count model is proposed for number of defects. Which property of the response supports that choice?

1. AFrequencies are sufficient for every quantitative variable, even when magnitude and dispersion are the substantive targets of the analysis.
2. BThe observational unit is whichever column has the most unique values.
3. COne row always represents one independent person, even when the table contains transactions, visits, or repeated measurements from the same person.
4. DCounts are typically discrete because their possible values are countable, even when a model approximates them with a continuous distribution.

Question 7 of 10

Which summaries naturally match a product category and which match a measured weight?

1. AA proportion may validly be modeled below zero or above one if the fitted curve is smooth, and a count may take negative fitted values without qualification.
2. BFrequencies are sufficient for every quantitative variable, even when magnitude and dispersion are the substantive targets of the analysis.
3. CMeans and standard deviations are the natural summaries for unordered category labels.
4. DMeans and standard deviations require quantitative meaning; frequencies and proportions are natural summaries for categorical variables.

Question 8 of 10

Account identifiers and transaction amounts are both stored as numbers, but only amounts have meaningful arithmetic differences. Which distinction determines their variable types and valid summaries?

1. ASummaries and models must match the variable type because category labels do not support the same arithmetic as measured quantities.
2. BSupport is determined only by the values observed in one sample, so unobserved but possible values are excluded from the variable definition.
3. CFrequencies are sufficient for every quantitative variable, even when magnitude and dispersion are the substantive targets of the analysis.
4. DMeans and standard deviations are the natural summaries for unordered category labels.

Question 9 of 10

Defect totals are nonnegative integer counts, yet a model offered as an exact description of them assigns probability to negative and fractional outcomes. Which property rules it out as an exact model?

1. AThe support of a variable includes its possible values and constraints, such as nonnegative counts or proportions bounded between zero and one.
2. BA proportion may validly be modeled below zero or above one if the fitted curve is smooth, and a count may take negative fitted values without qualification.
3. CSupport is determined only by the values observed in one sample, so unobserved but possible values are excluded from the variable definition.
4. DRounding a continuous measure to two decimals changes the underlying construct into a count.

Question 10 of 10

Temperature is physically continuous but stored to the nearest degree, so a finite file contains repeated integers. How should the underlying variable be classified?

1. AMeasurement resolution can make a recorded continuous quantity look discrete without changing the underlying quantity being measured.
2. BRounding a continuous measure to two decimals changes the underlying construct into a count.
3. CRepeated rounded values prove that the variable is nominal.
4. DA measured amount becomes categorical whenever analysts group it for a chart, and the discarded within-group magnitudes remain fully recoverable.