C955 Applied Probability and Statistics - Set 4 - Part 3

Correct Answer: Quantitative data are numeric measurements; qualitative data are categories

Quantitative data consist of numeric measurements or counts, while qualitative (categorical) data classify observations into categories such as color or type.

Correct Answer: Eye color

Eye color classifies observations into named categories and is qualitative. The others are numeric measurements and therefore quantitative.

Correct Answer: Discrete data are counted; continuous data are measured on a scale

Discrete data arise from counting and take separate values, while continuous data come from measurement and can take any value within a range.

Correct Answer: Ratio scale

A ratio scale has a true zero, so ratios are meaningful. Weight is an example: 20 kilograms is genuinely twice 10 kilograms.

Correct Answer: An interval scale lacks a true zero, so ratios are not meaningful

Interval scales such as Celsius temperature have equal intervals but no true zero, so 20 degrees is not twice as hot as 10 degrees in any absolute sense.

Correct Answer: Categories with a meaningful order but not necessarily equal spacing

Ordinal data have a natural ranking, such as survey ratings from poor to excellent, but the distances between categories are not necessarily equal.

Correct Answer: Categories with no inherent order

Nominal data classify observations into unordered categories, such as blood type or country of origin, where no category is inherently greater than another.

Correct Answer: Some calculations, such as the mean, are only meaningful for certain scales

Operations like computing a mean require numeric scales. Applying them to nominal categories, such as averaging color codes, produces meaningless results.

Correct Answer: Summarizing and describing the main features of a data set

Descriptive statistics summarize data through measures of center, spread, and shape and through graphs, in contrast to inferential statistics which generalize to populations.

Correct Answer: Drawing conclusions about a population from sample data

Inferential statistics use sample data to estimate parameters and test hypotheses about a larger population, quantifying the uncertainty in those conclusions.