A quality engineer measured 75 bolts. The length (in mm) and the number of flaws on each of 75 bolts is recorded.
(i) Identify the variable(s) in the study.
(ii) Explain the type of data for each variable in the study (e.g., categorical and ordinal, continuous or discrete, etc.).
(iii) Identify the observational unit.
(iv) Determine the sample size.

The variables in the conducted study are "length of bolt" and "number of flaws on each bolt" because quality engineer is interested in evaluating the length of bolt and the number of flaws each bolt is having. Thus, the length and number of flaws for each bolt varies and we can say that "length of bolt" and "number of flaws on each bolt" are two variables in the conducted study.

ii)

The length of bolt can be presented numerically and further that the length of a bolt is measurable and thus, the length of bolt is a quantitative continuous variable.

The number of flaws of each bolt can be presented numerically and further that the number of flaws of each bolt can be counted and thus, the number of flaws of each bolt is a quantitative discrete variable.

iii)

The conducted study indicates that observational units are "bolts" because for each bolt its length and flaws are determined.

iv)

The sample size is 75 because a quality engineer selected 75 bolts and then measured its length and flaws.