A researcher records each survey participant's phone area code (e.g., 212, 415, 617) to indicate which city they live in. What type of data is this?
AQuantitative discrete, because area codes are whole numbers
BQuantitative continuous, because you could interpolate between area codes
CCategorical, because arithmetic on area codes produces no meaningful result
DOrdinal, because higher area codes correspond to more populated regions
Despite being numbers, area codes are labels for geographic regions — not amounts of anything. The 'average area code' is meaningless. The test for quantitative data is whether arithmetic produces a meaningful result; here it does not. This is the central insight: looking like a number does not make something quantitative.
Question 2 Multiple Choice
A doctor records patient pain level two ways: Method A uses labels (mild/moderate/severe); Method B has patients report an exact 0–10 scale value. How do these variables differ in data type?
AMethod A is categorical (ordinal); Method B is quantitative — the 0–10 scale supports arithmetic
BBoth are categorical, because both measure the same underlying attribute
CBoth are quantitative, because both can be placed in order
DMethod A is nominal; Method B is ordinal — neither is truly quantitative
Same concept, two measurement approaches — two different data types. Method A's labels have order but no meaningful arithmetic (the gap between 'mild' and 'moderate' is not measured). Method B's numeric scale supports computing differences and averages. The attribute being measured doesn't determine the data type; the measurement scale does.
Question 3 True / False
Zip codes are categorical data even though they are composed entirely of digits.
TTrue
FFalse
Answer: True
Yes — zip codes are labels for geographic zones, not measurements of quantity. Averaging them (e.g., 10001 and 90210 averaging to 50106) produces a meaningless result. Numbers are categorical whenever arithmetic on them produces nonsense. Other examples: jersey numbers, telephone numbers, Social Security numbers, and 1/2/3 coded survey responses.
Question 4 True / False
Any variable that can be placed in ascending order is quantitative data.
TTrue
FFalse
Answer: False
Ordinal data can be ordered but is still categorical — it does not support arithmetic. Letter grades (A > B > C), pain levels (mild < moderate < severe), and Likert scale responses (disagree/neutral/agree) all have natural order without meaningful numeric differences between levels. Quantitative data requires not just ordering but meaningful arithmetic — differences and averages must make sense.
Question 5 Short Answer
A classmate reports: 'I computed the average zip code of our survey respondents — it's 52,317. This tells us something about the typical location.' What is wrong with this claim, and what analysis would be appropriate instead?
Think about your answer, then reveal below.
Model answer: Averaging zip codes is meaningless because zip codes are categorical labels, not quantities. The numeric value has no arithmetic meaning — the 'average' of two geographic labels is not a geographic location. An appropriate analysis would use counts and proportions: a frequency table or bar chart showing how many respondents came from each zip code or region.
This is the central trap of data types. The moment you perform arithmetic on a categorical variable, you've committed a category error. For categorical data, the right summaries are counts, proportions, and modes — not means or standard deviations. Recognizing this is the first filter in any data analysis workflow.