Question

exercises 1 - 2

1. explain the difference between qualitative variables and quantitative variables.
2. explain the difference between discrete and continuous variables.
3. why are continuous variables rounded when they are used in statistical studies?
4. name and define the four types of measurement levels used in statistics.

for exercises 5 - 10, determine whether the data are qualitative or quantitative.

1. sizes of soft drinks sold by a fast - food restaurant (small, medium, and large) qualitative
2. pizza sizes (small, medium, and large) qualitative
3. cholesterol counts for individuals quantitative
4. microwave wattage quantitative
5. number of degrees awarded by a college each year for the last 10 years quantitative
6. ratings of teachers qualitative

for exercises 11 - 16, determine whether the data are discrete or continuous.

1. number of phone calls received by a 911 call center each day discrete
2. systolic blood pressure readings continuous
3. weights of the suitcases of airline passengers on a specific flight continuous
4. votes received by mayoral candidates in a city election discrete
5. number of students in the mathematics classes during the fall semester at your school for a particular school year discrete
6. temperatures at a seashore resort continuous

for exercises 17 - 22, give the boundaries of each value.

1. 24 feet 23.5 - 24.5
2. 6.3 millimeters 6.25 - 6.35
3. 143 miles 142.5 - 143.5
4. 19.63 tons 19.625 - 19.635
5. 200.7 miles 200.65 - 200.75
6. 19 quarts 18.5 - 19.5

for exercises 23 - 30, classify each as nominal - level, ordinal - level, interval - level, or ratio - level measurement.

1. telephone numbers nominal
2. leap years: ... 2016, 2020, 2024, ... nominal
3. distances communication satellites in orbit are from earth ratio
4. scores on a statistical final exam ratio
5. rating of cooked ribs at a rib cook - off ordinal
6. blood types—o, a, b, ab nominal
7. online spending in dollars ratio
8. horsepower of automobile engines ratio

Explanation:

Step1: Define qualitative and quantitative variables

Qualitative variables describe qualities or characteristics and are non - numerical (e.g., colors, types). Quantitative variables are numerical and represent amounts or counts (e.g., number of students, height).

Step2: Define discrete and continuous variables

Discrete variables have distinct, separate values and can often be counted (e.g., number of cars in a parking lot). Continuous variables can take on any value within a certain range and are often measured (e.g., temperature, weight).

Step3: Explain rounding of continuous variables

Continuous variables are rounded in statistical studies because measurements are often made with instruments that have limited precision. Also, for simplicity and practicality in data analysis and reporting.

Step4: Name and define measurement levels

Nominal level: Categorical data with no order (e.g., gender, eye color). Ordinal level: Categorical data with an order (e.g., rankings like low - medium - high). Interval level: Numerical data with a fixed unit of measurement and no true zero (e.g., temperature in Celsius). Ratio level: Numerical data with a fixed unit of measurement and a true zero (e.g., height, weight).

Step5: Determine data type for exercises 5 - 10

1. Sizes of soft drinks are qualitative as they are non - numerical categories.
2. Pizza sizes are qualitative for the same reason.
3. Cholesterol counts are quantitative as they are numerical values.
4. Microwave wattage is quantitative as it is a numerical measurement.
5. Number of degrees awarded is quantitative as it is a count.
6. Ratings of teachers are qualitative as they are non - numerical assessments.

Step6: Determine discrete or continuous for exercises 11 - 16

1. Number of phone calls is discrete as it is a count of distinct events.
2. Systolic blood pressure is continuous as it can take on any value within a range.
3. Weights of suitcases are continuous as weight is a measured quantity.
4. Votes received is discrete as it is a count.
5. Number of students is discrete as it is a count.
6. Temperatures are continuous as they can take on any value within a range.

Step7: Find boundaries for exercises 17 - 22

1. For 24 feet, boundaries are 23.5 - 24.5.
2. For 6.3 millimeters, boundaries are 6.25 - 6.35.
3. For 143 miles, boundaries are 142.5 - 143.5.
4. For 19.63 tons, boundaries are 19.625 - 19.635.
5. For 200.7 miles, boundaries are 200.65 - 200.75.
6. For 19 quarts, boundaries are 18.5 - 19.5.

Step8: Classify measurement levels for exercises 23 - 30

1. Telephone numbers are nominal as they are just labels with no order or numerical meaning.
2. Leap years are interval as the difference between years is meaningful but there is no true zero year.
3. Distances of satellites from Earth are ratio as there is a true zero (distance = 0) and the measurements have a fixed unit.
4. Scores on a statistical final exam are ratio if there is a true zero (score of 0 means no correct answers) and a fixed unit.
5. Ratings of cooked ribs are ordinal as they have an order (e.g., 1 - 5 stars).
6. Blood types are nominal as they are non - numerical categories.
7. Online spending in dollars is ratio as there is a true zero (no spending) and a fixed unit.
8. Horsepower of automobile engines is ratio as there is a true zero (0 horsepower) and a fixed unit.

Answer:

1. Qualitative variables describe qualities, non - numerical; quantitative variables are numerical, represent amounts/counts.
2. Discrete have distinct values, counted; continuous can take any value in a range, measured.
3. Due to instrument precision and data - analysis practicality.
4. Nominal: categorical, no order; Ordinal: categorical, has order; Interval: numerical, no true zero; Ratio: numerical, true zero.
5. Qualitative
6. Qualitative
7. Quantitative
8. Quantitative
9. Quantitative
10. Qualitative
11. Discrete
12. Continuous
13. Continuous
14. Discrete
15. Discrete
16. Continuous
17. 23.5 - 24.5
18. 6.25 - 6.35
19. 142.5 - 143.5
20. 19.625 - 19.635
21. 200.65 - 200.75
22. 18.5 - 19.5
23. Nominal
24. Interval
25. Ratio
26. Ratio
27. Ordinal
28. Nominal
29. Ratio
30. Ratio