Analyzing categorical data #1 - Questions and Answers

Question 1 In a study, the data you collect is Gender What type of the data is this? Quantitative - Discrete Quantitative - Continuous Qualitative (Categorical) Answer Step 1 There are only specific or isolated values in the discrete data. The range set's values are all included in the continuous data. In categorical data, each person is assigned to one of a small, typically fixed number, of possible values. Step 2 Response: (Qualitative) The categorical data type variable is gender. Gender: "Male, Female" Because of how it is categorized, the information is categorical. Question 2 Why is hair color classified as categorical data? Answer Step 1 In categorical variable we simply assign labels for identification. Categorical values are discrete in nature and it belongs to a particular finite set of categories or classes. Step 2 Hair colour is a categorical variable because here we assign the labels such as black, brown, white etc. In this case colours such as brown, black, white are categories which are discrete in nature. There are 3 sets of categories here. Among categories, there is no particular order, so it is Nominal variable. Question 3 Which statement best characterizes the definitions of categorical and quantitative data? Quantitative data consist of numbers, whereas categorical data consist of names and labels that are not numeric. Quantitative data consist of numbers representing measurements or counts, whereas categorical data consist of names or labels Quantitative data consist of values that can be arranged in order, whereas categorical data consist of values that cannot be arranged in order. Quantitative data have an uncountable number of possible values, whereas categorical data have a countable number of possible values. Answer Step 1 A data is said to be quantitative data if it can be measured on numeric or quantitative scale. Mathematical operations can be performed on the quantitative variables. A data is said to be categorical data if it can classify the observations as names or labels. Mathematical operations cannot be performed on the categorical variables. Step 2 Reason for correct answer: According to the definitions, the quantitative data consist of numbers that represent measurements or counts and categorical data consist of names and labels. Thus, second option is correct. Reason for incorrect answer: Categorical data consist of names and labels, and that can be numeric. Such as, age groups. For example the age groups 20-30, 30-40, 40-50 etc. categorize the variable age, the jersey number of a football player is numerical, but it labels the player. Hence, first option is not correct. Quantitative data can be arranged in numerical order and some categorical data can be arranged in logical order. Thus, third option is not correct. Quantitative and categorical data, both have countable number of possible values. Thus, fourth option is not correct. Question 4 Quantitative/Categorical Data Identify each of the following as quantitative data or categorical data. a. The platelet counts in Data Set 1 "Body Data" in Appendix B b. The cigarette brands in Data Set 13 "Cigarette Contents" in Appendix B c. The colors of the M&M candies in Data Set 27 "M&M Weights" in Appendix B d. The weights of the M&M candies in Data Set 27 "M&M Weights" in Appendix B Answer Qualitative variables are those variables that define a trait or attribute with unique categories. In other words, based on the feature, these factors split the instances into two or more groups. For instance, the literacy rate is a categorical variable if the participants are categorized based on that figure. Quantitative data: A quantitative variable is one that keeps track of a numerical number. To put it another way, these variables may be measured or tallied. Some examples of quantitative variables include student heights, land area, and people's ages. (a) The platelet counts represent the numbers and that can be counted or measured. Thus, the data set is quantitative data. (b) The cigarette brands represent the different categories. Thus, the data set is Categorical data. (c) The color of M&M brands represents the different categories. That is, red, orange, yellow, brown, blue and green. Thus, the data set is Categorical data. (d) The weights of M&M candies represent the numbers and that can be counted or measured. Thus, the data set is quantitative data.