Classify each as nominal-level, ordinal-level, interval-level, or ratio-level measurement.
a. Pages in the city of Cleveland telephone book.
b. Rankings of tennis players.
c. Weights of air conditioners.
d. Temperatures inside 10 refrigerators.
e. Salaries of the top five CEOs in the United States.
f. Ratings of eight local plays (poor, fair, good, excellent).
g. Times required for mechanics to do a tune-up.
h. Ages of students in a classroom.
i. Marital status of patients in a physician’s office.
j. Horsepower of tractor engines.
The correct answer and explanation is :
Sure! Here’s the classification along with a detailed explanation:
Measurement Level Classifications:
a. Pages in the city of Cleveland telephone book – Ratio
b. Rankings of tennis players – Ordinal
c. Weights of air conditioners – Ratio
d. Temperatures inside 10 refrigerators – Interval
e. Salaries of the top five CEOs in the United States – Ratio
f. Ratings of eight local plays (poor, fair, good, excellent) – Ordinal
g. Times required for mechanics to do a tune-up – Ratio
h. Ages of students in a classroom – Ratio
i. Marital status of patients in a physician’s office – Nominal
j. Horsepower of tractor engines – Ratio
Explanation (300 words):
Understanding levels of measurement helps determine what kind of statistical analysis is appropriate. There are four main levels: nominal, ordinal, interval, and ratio.
Nominal level is the lowest; it classifies data into distinct categories without any order. For example, marital status (i) only labels individuals (e.g., single, married) without implying any order.
Ordinal level data involves order or ranking but does not measure the exact difference between ranks. Tennis player rankings (b) and ratings of plays (f) fall into this category. While we know the order (e.g., excellent > good), we don’t know the precise difference between them.
Interval level has ordered categories with known, equal intervals between values, but no true zero point. Temperatures in refrigerators (d) are interval because 0°F does not mean “no temperature.” You can measure differences but not ratios.
Ratio level includes all properties of interval data, plus a meaningful zero point, which allows for comparison using multiplication or division. Weights (c), ages (h), times (g), horsepower (j), salaries (e), and number of pages (a) are all ratio data. A weight of 0 means no weight, and 20 lbs is twice as heavy as 10 lbs.
In summary, nominal is categorical with no order, ordinal is ordered without meaningful intervals, interval has ordered and evenly spaced values but no true zero, and ratio has all of those properties including a true zero, enabling the most comprehensive statistical analysis.
