# Indicate whether the following variables are categorical or numerical? If they are numerical, state whether they are discrete or continuous. (a) The price of randomly selected sweaters in a department store. (b) The first three digits of the social security number of randomly selected US residents. The eye color of randomly selected Columbia students. (c) The number of views of randomly selected YouTube videos. The speed of randomly selected cars on Broadway.

Question
Analyzing categorical data
Indicate whether the following variables are categorical or numerical? If they are numerical, state whether they are discrete or continuous.
(a) The price of randomly selected sweaters in a department store.
(b) The first three digits of the social security number of randomly selected US residents. The eye color of randomly selected Columbia students.
(c) The number of views of randomly selected YouTube videos. The speed of randomly selected cars on Broadway.

2021-02-09
Step 1
Numerical data are also known as quantitative data that can be expressed in terms of numbers, whether discrete or continuous. Discrete data take integral values that are countable finite or infinite. Continuous data takes all numerical value on a number line viz. fractions or decimals. Examples of discrete data are Nuber of students, in a class, no of sands in a beach. Example of continuous data is weight and heights of school-going students. Level of measurement for numerical data is usually interval or ratio.
Categorical data are also known as qualitative data. They display qualitative characteristics like beauty, honesty, hence also known as attribute data. The level of measurement for categorical data is nominal or ordinal as they can either be named or ranked in terms of a particular order of preference.
Step 2
(a) The price of randomly selected sweaters in a department store are numerical Data. Since each sweater can be counted as a definite non-negative integral value, hence it is a discrete numerical variable.
(b) The first three digits of the social security numbers are categorical variable. This is because, although they consist of numbers they are used for identification of peoples and not for any algebraic treatment.
The eye colour of randomly selected Columbian students is a categorical variable. This is because qualitative or categorical variables—such as gender, hair colour, or ethnicity are used to group individuals
(c) The number of views of randomly selected YouTube videos is a discrete numerical variable. This is because the number is countable whether finite or countably infinite.
The speed of randomly selected cars on Broadway is a continuous numerical variable. This because speed can take any value (like 120 mph, 120.1 mph,120.2 mph and so on) if it is measured with an appropriate and accurate gauge.

### Relevant Questions

For each of the following variables, indicate whether they are categorical or numerical. Also, write down what type of graph can be drawn for each.
a) Position of a university staff members.
b) Weight of participants.
C Air temperature on the Celsius scale
D) The daily number of code lines written by a programmer
In each of the following, identify the variables are categorical nominal, or categorical ordinal, or numerical discrete or numerical continuous.
2.Pant size of a randomly selected male as S, M, L, XL, XXL.
In each of the following, identify the variables are categorical nominal, or categorical ordinal, or numerical discrete or numerical continuous.
1.Political affiliation of a voter
A wallstreet journal subcriber survey asked 46 questions about subcribers characteristics and interest. State whether each of the following questions provides categorical or quantitative data.
b. Are you male or females?
c. When did you first start reading the WSJ? High school , college, early career, midcareer, late career, or retirement?
d. How long have you been in your present job or position?
e. What type of vehicle are you considering for you next purchase? Nine response categories include sedan, sports car, SUV, minivan, and so on.
The school cafeteria collects data on students’ juice box selections. What type of data are these?
1.categorical, nominal data
2.numerical, discrete data
3.categorical, ordinal data
4.numerical, continuous data
Is the gift you purchased for that special someone really appreciated? This was the question investigated in the Journal of Experimental Social Psychology (Vol. 45, 2009). Toe researchers examined the link between engagement ring price (dollars) and level of appreciation of the recipient $$\displaystyle{\left(\text{measured on a 7-point scale where}\ {1}=\ \text{"not at all" and}\ {7}=\ \text{to a great extent"}\right)}.$$ Participants for the study were those who used a popular Web site for engaged couples. The Web site's directory was searched for those with "average" American names (e.g., "John Smith," "Sara Jones"). These individuals were then invited to participate in an online survey in exchange for a \$10 gift certificate. Of the respondents, those who paid really high or really low prices for the ring were excluded, leaving a sample size of 33 respondents. a) Identify the experimental units for this study. b) What are the variables of interest? Are they quantitative or qualitative in nature? c) Describe the population of interest. d) Do you believe the sample of 33 respondents is representative of the population? Explain. e. In a second, designed study, the researchers investigated whether the link between gift price and level of appreciation was stronger for birthday gift givers than for birthday gift receivers. Toe participants were randomly assigned to play the role of gift-giver or gift-receiver. Assume that the sample consists of 50 individuals. Use a random number generator to randomly assign 25 individuals to play the gift-receiver role and 25 to play the gift-giver role.
The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an information source for the U.S. Department of Transportation. In one part of the survey the person being interviewed was asked to respond to the following statement: "Drivers of motor vehicles should be allowed to talk on a hand-held cell phone while driving." Possible responses were strongly agree, some what agree, some what disagree, and strongly disagree. Forty-four respondents said that they strongly agree with this statement, 120 said that they some what agree, 165 said they some what disagree, and 755 said they strongly disagree with this statement.
Do the responses for this statement provide categorical or quantitative data?
Select the best suitable answer. If none of the choices represents a correct answer, select “Other” and write your own answer. The school cafeteria collects data on students’ juice box selections. This is an example of
A numerical, ordinal data.
B numerical, nominal data.
C categorical, ordinal data.
D categorical, nominal data.
Discrete or Continuous? II Identify the following as discrete or continuous random variables:
a.Number of overdue accounts in a department store at a particular time
The Kroger Company is one of the largest grocery retailers in the United States, with over 2000 grocery stores across the country. Kroger uses an online customer opinion questionnaire to obtain performance data about its products and services and learn about what motivates its customers (Kroger website, April 2012). In the survey, Kroger customers were asked if they would be willing to pay more for products that had each of the following four characteristics.
The four questions were: Would you pay more for:
products that have a brand name?
products that are environmentally friendly?
products that are organic?
products that have been recommended by others?
For each question, the customers had the option of responding Yes if they would pay more or No if they would not pay more.
a. Are the data collected by Kroger in this example categorical or quantitative?
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