Assignment 2 581

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Central Michigan University *

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581

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Marketing

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Feb 20, 2024

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Uploaded by KidZebraMaster825

1. Cycle Time Distribution Analysis The histogram suggests a right-skewed distribution, indicating that most delivery processes are completed within a shorter timeframe, with a concentration of data on the lower end of the scale. However, the presence of a long tail to the right hints at occasional delays, pointing to a subset of processes that are less efficient. The statistical values provide further insights: a kurtosis value of -0.1005 suggests a flatter distribution with fewer outliers than a normal distribution, while the mean and median values, 3.9733 and 4 respectively, corroborate the skewness seen in the histogram. The skewness value of -0.5039, which unusually suggests a left skew, may imply a discrepancy or an atypical aspect of the distribution not immediately apparent from the histogram. Finally, a standard deviation of 1.7044 indicates moderate variability in cycle times. These metrics combined reflect a system that operates effectively in general but also reveal inefficiencies that, if addressed, could enhance operational reliability and customer satisfaction. 2. Sales and Profit Distribution by Sub-category Analysis

Analysis Sales vs Subcategory: The data shows sales information across different sub-categories. The highest sale that is not an outlier is 1252.7 units, while the lowest sale not considered an outlier is 27.41 units. Outliers in sales are points that are much higher or lower than most of the other sales numbers; for example, some sales are as high as 2025, 2405, and 9893 units. In the boxplot image, each sub-category, like Accessories, Appliances, and so on, has a box that shows the middle range of sales. The line in the middle of the box is the median, which is the middle sale value. Outliers are shown as dots; these are sales that are unusually high or low compared to other sales in the same sub-category. For example, in 'Copiers', you can see a few high sales that stand out from the rest. These are much higher than most sales in 'Copiers' and are marked as outliers. This could mean that a few copiers sold a lot more than others. Overall, the boxplot shows that some sub-categories have a wide range of sales, with some very high or very low sales compared to the median. This information could help a business understand which products sell consistently and which ones have more varied sales.

Profit vs SubCategory: The information given tells us about the profits for different categories of products sold. Accessories, Art, and Envelopes have small losses or profits at the lowest end, while categories like Appliances, Binders, and Machines sometimes show much bigger losses. On the flip side, products like Copiers can bring in the most profit, with the highest recorded profit being around 8399 units. Looking at the range of profits across all categories, we can see that selling Machines and Copiers can be quite unpredictable – sometimes they can lose a lot of money, and other times they can make a lot. Meanwhile, selling items like Paper and Labels is more consistent, with profits not changing too much. In summary, this data helps a business to see which products have stable earnings and which ones have the potential for high rewards but also high risks. Understanding this can help the business make better choices about what products to focus on or what strategies to change. 3. Sales and Profit Distribution by Customer Segment Analysis

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Sales vs Segment: The boxplot shows the lowest and highest sales for three different customer groups: Consumer, Corporate, and Home Office. For the Consumer group, the lowest sales figure is a loss of about 6599 units, and the highest sales figure is a gain of about 4946 units. For the Corporate group, the range is from a loss of about 2929 units to a gain of about 8399 units. The Home Office group's sales range from a loss of about 1143 units to a gain of about 3919 units. When we look at these numbers, we see that the Corporate group has the potential for the highest sales, but also a significant risk of loss. The Consumer group has the lowest potential sales gain, but its biggest loss is the largest among the three groups. The Home Office group has the smallest range of sales, meaning their sales are more consistent compared to the other two groups. This information is useful for understanding which group brings in the most sales and which group has the most stable sales. It can help a business decide where to focus their efforts and how to manage the risks of selling to each group.

Profit vs Segment: Analyzing the sales and profit data for different customer segments— Consumer, Corporate, and Home Office—we can see a varied performance. The Consumer segment has recorded the highest loss at approximately 6600 units, but also a substantial gain, with the highest profit close to 4946 units. The Corporate segment, while having a lower recorded loss at about 2929 units, shows the highest profit among the segments, reaching nearly 8400 units. The Home Office segment shows losses and profits on a smaller scale than the Corporate, with losses around 1143 units and profits up to almost 3920 units. What stands out in this data are the outliers, which are the extreme values that don't fit the general pattern of the data. For instance, while most profits in the Corporate segment are within a predictable range, there are a few cases where the profit has been exceptionally high. These outliers are important because they can indicate unusual success or issues that need attention. This information is crucial for a business, as it highlights the potential for high profits in the Corporate segment, suggests that Consumer sales can be quite volatile, and indicates more consistency in the Home Office segment. By understanding these patterns and outliers, a business can tailor its strategies to each customer segment, potentially reducing risks and maximizing profits.

R Code #Installing the package e1071 for kurtosis and skewness install.packages("e1071") #Importing the library for Skewness and Kurtosis library(e1071) #Importing library for Box Plot library(ggplot2) #Finding Mean Value mean_value <- mean(Sales_gl$`Cycle time`) #Finding median Value median_value <- median(Sales_gl$`Cycle time`) #Finding Standard deviation standard_deviation <- sd(Sales_gl$`Cycle time`) #Finding Skewness skewness_value <- skewness(Sales_gl$`Cycle time`) #Finding Kurtosis Value kurtosis_value <- kurtosis(Sales_gl$`Cycle time`) #Plotting Histogram for Cycle time hist(Sales_gl$`Cycle time`, main= 'Histogram of Cycle Time', xlab="Cycle Time", ylab="Frequency", col ="blue", border="black", breaks=20) #Plotting BoxPlot for Sales and Sub-Category of the products boxplot(Sales ~ `Sub-Category`, data = Sales_gl, main = "Sales vs Sub Category Plot", xlab = "Sub-category", ylab = "Sales", breaks= 40, col='black')

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# Create the boxplot object for each level of Sub-Category without plotting it boxplot_Sales_Subcat <- boxplot(Sales ~ `Sub-Category`, data = Sales_gl, plot = FALSE) # Initialize vectors to store the lowest and highest points lowest_points_sales_Subcat<- numeric(length = length(boxplot_Sales_Subcat$names)) highest_points_sales_Subcat <- numeric(length = length(boxplot_Sales_Subcat$names)) # Loop over each sub-category to extract the points for(i in seq_along(boxplot_Sales_Subcat$names)) { # Stats for the current sub-category stats <- boxplot_Sales_Subcat$stats[,i] # The lowest non-outlier for the current sub-category lowest_non_outlier_sales_Subcat <- stats[1] # The highest non-outlier for the current sub-category highest_non_outlier_sales_Subcat<- stats[5] # Outliers for the current sub-category outliers <- boxplot_Sales_Subcat$out[boxplot_Sales_Subcat$group == i] # Absolute minimum and maximum, including outliers, for the current sub-category lowest_points_sales_Subcat[i] <- if(length(outliers) > 0) min(c(lowest_non_outlier_sales_Subcat, outliers)) else lowest_non_outlier_sales_Subcat highest_points_sales_Subcat[i] <- if(length(outliers) > 0) max(c(highest_non_outlier_sales_Subcat, outliers)) else highest_non_outlier_sales_Subcat_sales_Subcat } # Combine the lowest and highest points with the names of the sub-categories extreme_points_sales_Subcat <- data.frame(Sub_Category = boxplot_Sales_Subcat$names, Lowest_Point = lowest_points_sales_Subcat, Highest_Point = highest_points_sales_Subcat) # Print the extreme points for each sub-category print(extreme_points_sales_Subcat) #Plotting BoxPlot forcProfit and Sub-Category of the products boxplot(Profit ~ `Sub-Category`, data = Sales_gl, main = "Profit vs Sub Category Plot", xlab = "Sub-category",

ylab = "Profit", col='black') # Create the boxplot object for each level of Sub-Category without plotting it boxplot_Profit_Subcat <- boxplot(Profit ~ `Sub-Category`, data = Sales_gl, plot = FALSE) # Initialize vectors to store the lowest and highest points lowest_points_profit_Subcat<- numeric(length = length(boxplot_Profit_Subcat$names)) highest_points_profit_Subcat <- numeric(length = length(boxplot_Profit_Subcat$names)) # Loop over each sub-category to extract the points for(i in seq_along(boxplot_Profit_Subcat$names)) { # Stats for the current sub-category stats <- boxplot_Profit_Subcat$stats[,i] # The lowest non-outlier for the current sub-category lowest_non_outlier_profit_Subcat <- stats[1] # The highest non-outlier for the current sub-category highest_non_outlier_profit_Subcat<- stats[5] # Outliers for the current sub-category outliers <- boxplot_Profit_Subcat$out[boxplot_Profit_Subcat$group == i] # Absolute minimum and maximum, including outliers, for the current sub-category lowest_points_profit_Subcat[i] <- if(length(outliers) > 0) min(c(lowest_non_outlier_profit_Subcat, outliers)) else lowest_non_outlier_profit_Subcat highest_points_profit_Subcat[i] <- if(length(outliers) > 0) max(c(highest_non_outlier_profit_Subcat, outliers)) else highest_non_outlier_profit_Subcat_profit_Subcat } # Combine the lowest and highest points with the names of the sub-categories extreme_points_profit_Subcat <- data.frame(Sub_Category = boxplot_Profit_Subcat$names, Lowest_Point = lowest_points_profit_Subcat, Highest_Point = highest_points_profit_Subcat) # Print the extreme points for each sub-category print(extreme_points_profit_Subcat) #Plotting BoxPlot for Sales and Customer Segment boxplot(Sales ~ Segment, data = Sales_gl, main = "Sales vs Segment Plot", xlab = "Segment",

ylab = "Sales", col='black') # Create the boxplot object for each level of Sub-Category without plotting it boxplotSales_Segment <- boxplot(Profit ~ Segment, data = Sales_gl, plot = FALSE) # Initialize vectors to store the lowest and highest points lowest_pointsSales_Segment<- numeric(length = length(boxplotSales_Segment$names)) highest_pointsSales_Segment <- numeric(length = length(boxplotSales_Segment$names)) # Loop over each sub-category to extract the points for(i in seq_along(boxplotSales_Segment$names)) { # Stats for the current sub-category stats <- boxplotSales_Segment$stats[,i] # The lowest non-outlier for the current sub-category lowest_non_outlierSales_Segment <- stats[1] # The highest non-outlier for the current sub-category highest_non_outlierSales_Segment<- stats[5] # Outliers for the current sub-category outliers <- boxplotSales_Segment$out[boxplotSales_Segment$group == i] # Absolute minimum and maximum, including outliers, for the current sub-category lowest_pointsSales_Segment[i] <- if(length(outliers) > 0) min(c(lowest_non_outlierSales_Segment, outliers)) else lowest_non_outlierSales_Segment highest_pointsSales_Segment[i] <- if(length(outliers) > 0) max(c(highest_non_outlierSales_Segment, outliers)) else highest_non_outlierSales_SegmentSales_Segment } # Combine the lowest and highest points with the names of the sub-categories extreme_pointsSales_Segment <- data.frame(Sub_Category = boxplotSales_Segment$names, Lowest_Point = lowest_pointsSales_Segment, Highest_Point = highest_pointsSales_Segment) # Print the extreme points for each sub-category print(extreme_pointsSales_Segment) #Plotting BoxPlot for Profit and Customer Segment boxplot(Profit ~ Segment, data = Sales_gl, main = "Profit vs Segment Plot", xlab = "Segment",

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ylab = "Profit", col='black') # Create the boxplot object for each level of Sub-Category without plotting it boxplotProfit_Segment <- boxplot(Profit ~ Segment, data = Sales_gl, plot = FALSE) # Initialize vectors to store the lowest and highest points lowest_pointsProfit_Segment<- numeric(length = length(boxplotProfit_Segment$names)) highest_pointsProfit_Segment <- numeric(length = length(boxplotProfit_Segment$names)) # Loop over each sub-category to extract the points for(i in seq_along(boxplotProfit_Segment$names)) { # Stats for the current sub-category stats <- boxplotProfit_Segment$stats[,i] # The lowest non-outlier for the current sub-category lowest_non_outlierProfit_Segment <- stats[1] # The highest non-outlier for the current sub-category highest_non_outlierProfit_Segment<- stats[5] # Outliers for the current sub-category outliers <- boxplotProfit_Segment$out[boxplotProfit_Segment$group == i] # Absolute minimum and maximum, including outliers, for the current sub-category lowest_pointsProfit_Segment[i] <- if(length(outliers) > 0) min(c(lowest_non_outlierProfit_Segment, outliers)) else lowest_non_outlierProfit_Segment highest_pointsProfit_Segment[i] <- if(length(outliers) > 0) max(c(highest_non_outlierProfit_Segment, outliers)) else highest_non_outlierProfit_SegmentProfit_Segment } # Combine the lowest and highest points with the names of the sub-categories extreme_pointsProfit_Segment <- data.frame(Sub_Category = boxplotProfit_Segment$names, Lowest_Point = lowest_pointsProfit_Segment, Highest_Point = highest_pointsProfit_Segment) # Print the extreme points for each sub-category print(extreme_pointsProfit_Segment)

Assignment 2 581

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