1.2 Types of Data
Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, the hair colors of respondents are identified as 10 for brown hair, 20 for blond hair, 30 for black hair, and 40 for anything else. The average (mean) is calculated for 675 respondents and the result is 22.3. What is wrong with this calculation?
- The data are at the nominal level of measurement. - Such data are not counts or measures of anything, so it makes no sense to compute their average (mean).
Determine whether the given value is from a discrete or continuous data set. When a car is randomly selected, it is found to have a length of 17.75 ft.
A continuous data set because there are infinitely many possible values and those values cannot be counted.
Which of the following is associated with a parameter? A. Data that were obtained from an entire population. B. Data that were obtained from a voluntary poll at the end of a service call. C. A numerical measurement describing some characteristic of a sample. D. Data that were obtained from a sample.
A. Data that were obtained from an entire population.
Which of the following would be classified as categorical data? Hair color Number of suitcases on a plane Amount of rainfall Tree height
Hair Color
Which level of measurement consists of categories only where data cannot be arranged in an ordering scheme? Interval Ratio Ordinal Nominal
Nominal
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Monthly rainfall: 3.4 in, 3.6 in, 3.8 in, 4 in, and 4.2 in
Ratio
Determine whether the underlined number is a statistic or a parameter. A sample of students is selected and it is found that 40% own a vehicle.
Statistic because the value is a numerical measurement describing a characteristic of a sample.
State whether the data described below are discrete or continuous, and explain why. The exact masses of iron ore produced by different iron mines in a given period of time
The data are continuous because the data can take on any value in an interval.
State whether the data described below are discrete or continuous, and explain why. The heights (in feet) of different buildings
The data are continuous because the data can take on any value in an interval.
State whether the data described below are discrete or continuous, and explain why. The numbers of murders in different cities in a certain year
The data are discrete because the data can only take on specific values
Determine whether the data described below are qualitative or quantitative and explain why. The prices of a gallon of gasoline at the gas stations of a certain city
The data are quantitative because they consist of counts or measurements.
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Bushels of wheat
The ratio level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is a natural starting zero point.
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Miles of road
The ratio level of measurement is most appropriate because the data can be ordered, differences can be found and are meaningful, and there is a natural starting zero point.
A particular country has 60 total states. If the areas of all 60 states are added and the sum is divided by 60, the result is 206,482 square kilometers. Determine whether this result is a statistic or a parameter.
The result is a parameter because it describes some characteristic of a population.
