The accompanying data set contains three variables, x₁, x₂, and x₃. 

a. The variable x₁ contains 6 categories ranging from “A” to “F.” Reduce the number of categories to five by combining the two least-frequent categories. Name the new category “Other.” How many observations are in the “Other” category? 

b. The variable x₂ contains six categories ranging from “A” to “F.” This variable is ordinal, meaning that the categories are ordered. “A” represents the lowest level, whereas “F” represents the highest level. Replace the category names with category scores ranging from 1 (lowest) to 6 (highest). What is the average category score for x₂? 

c. The variable x₃ contains four unordered categories. To facilitate subsequent analyses, we need to convert x₃ into dummy variables. How many dummy variables should be created? Create the dummy variables using Category1 as the reference category.