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

a. Bin the values of x₁, x₂, and x₃ into five equal-size groups. Label the groups with numbers 1 (lowest) to 5 (highest). 

b. Combine the group labels of x₁, x₂, and x₃ to create a score like the RFM score described in Example 2.4. How many observations have the score “431”? How many observations have the score “222”?

Data from Example 2.4

In order to better understand her customers, Catherine Hill would like to perform the RFM analysis, a popular marketing technique used to identify high-value customers. RFM stands for recency, frequency, and monetary. The RFM ratings can be created from the Days Since Last (recency), Num Of Orders (frequency), and Spending2018 (monetary) variables. 

Following the 80/20 business rule (i.e., 80% of your business comes from 20% of your best customers), for each of the three RFM variables, Catherine would like to bin customers into five equal-size groups, with 20% of the customers included in each group. Each group is also assigned a score from 1 to 5, with 5 being the highest. Customers with the RFM rating of 555 are considered the most valuable customers to the company. 

In addition to the RFM binning, Catherine would like to bin the Income variable into five equal intervals. Finally, she would like to start a tiered membership status where different services and rewards are offered to customers depending on how much they spent in 2018. She would like to assign the bronze membership status to customers who spent less than $250, silver membership status to those who spent $250 or more but less than $1,000, and the gold membership status to those who spent $1,000 or more.