Question

graphical analysis in exercises 25 - 28, identify the level of measurement of the data listed on the horizontal axis in the graph.

1. over the next few years, how likely is it that the united states will enter a 1930s - like depression? (source: rasmussen reports)
2. average january snowfall for 15 cities (source: national climatic data center)
3. gender profile of the 111th congress (source: congressional research service)
4. motor vehicle accidents by year (source: national safety council)
5. the following items appear on a physicians intake form. identify the level of measurement of the data.

a. temperature
b. allergies
c. weight
d. pain level (scale of 0 to 10)

1. the following items appear on an employment application. identify the level of measurement of the data.

a. highest grade level completed
b. gender
c. year of college graduation
d. number of years at last job
extending concepts

1. writing what is an inherent zero? describe three examples of data sets that have inherent zeros and three that do not.
2. writing describe two examples of data sets for each of the four levels of measurement. justify your answer.

Explanation:

The levels of measurement are nominal, ordinal, interval, and ratio. Nominal data is categorical with no order (e.g., gender). Ordinal data has an order but no consistent interval between values (e.g., response levels like very likely, somewhat likely). Interval data has consistent intervals but no true zero (e.g., temperature in Celsius). Ratio data has a true zero and consistent intervals (e.g., weight, number of years at a job).

• For 25: The response categories ("very likely", "somewhat likely", etc.) are ordinal as they have an order but no consistent numerical difference between them.
• For 26: Snowfall amount is ratio data as it has a true zero (no snowfall) and consistent intervals (inches).
• For 27: Gender is nominal data as it is a categorical variable with no order.
• For 28: Year is an interval variable as the difference between years is consistent but there is no true zero in the sense of the scale starting from a non - arbitrary zero for the purpose of this data.
• For 29a: Temperature is interval (e.g., Celsius or Fahrenheit have no true zero in the sense that 0 degrees doesn't mean absence of temperature).
• For 29b: Allergies are nominal as they are categorical.
• For 29c: Weight is ratio as it has a true zero.
• For 29d: Pain level on a 0 - 10 scale is ordinal as the intervals may not be truly consistent in a physical sense and it's more about the order.
• For 30a: Highest grade level completed is ordinal as it has an order.
• For 30b: Gender is nominal.
• For 30c: Year of college graduation is interval.
• For 30d: Number of years at last job is ratio as it has a true zero.

Answer:

1. Ordinal
2. Ratio
3. Nominal
4. Interval

29a. Interval
29b. Nominal
29c. Ratio
29d. Ordinal
30a. Ordinal
30b. Nominal
30c. Interval
30d. Ratio