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## Summary Statistics for Delivery Time, Customer Satisfaction, and Sales Price

AuCement produces many types of cement products at its factory in Sydney and sells them in Sydney, Brisbane, Canberra, and Melbourne. Six month ago, the company established a new cement facility to load a new 20Kg packaged cement. The company sells this new product in a competitive price and has boosted its sales with this option. In every contract the price of the product is paid based on its delivery time and customer satisfaction. To investigate more about the sales, they surveyed the customers who have purchased this kind of cement and a sample of 50 receipts was selected from the previous sales. For better comparison, they scaled the delivery time with dividing the hours spent for delivering the product by the travelled kilometres. AuCement file contains data showing the customer’s location, the payment type, the delivery time, the amount of customer satisfaction, and the price of sales paid for every tonne of this product by each of the 50 customers.

AuCement would like to use the sample data to determine whether customers who receive their package earlier and are more satisfied about the quality also pays higher prices. The company would also like to investigate the effect that the customer location and the payment type have on sales.

Managerial Report

Use the methods of descriptive statistics to learn about the customers who purchase in higher prices. Include the following in your report:

• Graphical and numerical summaries for the length of delivery time, the customer satisfaction factor, and the average amount gained per sale. Discuss what you learn about AuCement’s new product sales based on this data.

(Hint: for the graphical summaries show histograms for each variable and for the numerical summaries draw a table listing mean, median, standard deviation, min, max and range for each variable)

• Summarise the frequency, the average sale price, average delivery time, and average customer satisfaction for each city. Discuss the observations you can make about AuCement’s business based on the destination city of the sales?
• Develop a scatter diagram, and compute the sample correlation coefficient to explore the relationship between the delivery time and the selling price. Use the horizontal axis for the delivery time of the new product. Discuss your findings.
• Develop a scatter diagram, and compute the sample correlation coefficient to explore the relationship between the delivery time and the customer satisfaction. Use the horizontal axis for the delivery time of the new product. Discuss your findings.
• Develop a scatter diagram, and compute the sample correlation coefficient to explore the relationship between the customer satisfaction and the sale price of new product. Use the horizontal axis to represent the customer satisfaction. Discuss your findings.

Ambulance Victoria has an official Response Time (RT) targets: Respond to incidents within 15 minutes for 85% of incidents state-wide. Response times are an important measure of the service they provide. The response times are measured from the receipt of the triple zero (000) call until paramedics arrive on scene. Response times are influenced by many factors including traffic, distance required to travel, availability of ambulances and demand for the services. They designate those patients that require urgent paramedic and hospital care as "Code 1," and these patients receive a "lights and sirens" response. The AmbulanceVictoria file provides information about their Code 1 response time performance by Local Government Area (LGA) in the 3rdquarter of the financial year 2015-2016.

Managerial Report

Use the data-visualization methods presented in this chapter to explore these data and discover relationships between the variables. Include the following in your report:

• Create a scatter chart to examine the relationship between the average response time and the total number of incidents. Include a trend line for this scatter chart with its formula. What does the scatter chart indicate about the average response time over the total number of incidents for these Victoria’s LGAs?
• Create a scatter chart to examine the relationship between the percentage of less than 15 minutes response times and the average response time. What does this scatter chart indicate about the relationship between the percentage of less than 15 minutes response times and the average response time?
• Create frequency distributions, percent frequency distributions and intervals in a table for the number of incidents using bin size of 250 incidents. Then, draw a histogram for the frequencies. Interpret the results. Do any data points appear to be outliers in this distribution?
• Create a PivotTable for these data. Use the PivotTable to generate a cross tabulation for LGA categories and rating. Determine which combinations of LGA categories and rating are most represented in the Ambulance Victoria data. Now filter the data to consider only area with average response time more than 15 minutes (900 seconds). What combinations of LGA categories and rating are most represented? What does this indicate about how the ranking of the LGAs may be defined for the other quarters of the year?
• Use the PivotTable to display the average incidents happened in each combination of category-rating pair of areas in the data set. Interpret the results.
Summary Statistics for Delivery Time, Customer Satisfaction, and Sales Price
1. The histogram and the summary statistics for the variable length of delivery time is shown below:

 Delivery time (minutes/ton.km) count 50 mean 0.3788 sample variance 0.0329 sample standard deviation 0.1813 minimum 0.09 maximum 0.82 range 0.73 skewness 0.5333 kurtosis -0.1401 coefficient of variation (CV) 47.86% 1st quartile 0.2300 median 0.3550 3rd quartile 0.4775 interquartile range 0.2475 mode 0.3200

According to the summary statistics, the mean delivery time is 0.3788 minutes/ton.km, The range of the delivery time is 0.73 minutes/ton.km.

The Histogram and summary statistics for the variable Customer satisfaction is shown below:

 Customer satisfaction count 50 mean 5.10 sample variance 4.05 sample standard deviation 2.01 minimum 1 maximum 10 range 9 skewness 0.14 kurtosis 0.08 coefficient of variation (CV) 39.46% 1st quartile 4.00 median 5.00 3rd quartile 6.00 interquartile range 2.00 mode 5.00

According to the summary statistics, the mean customer satisfaction is 5.10, The range of the customer satisfaction is 9 and the standard deviation is 2.01.

The Histogram and summary statistics for the variable Sales Price is shown below:

 Sale price (\$/ton) count 50 mean 404.18 sample variance 1,760.72 sample standard deviation 41.96 minimum 345 maximum 520 range 175 skewness 0.70 kurtosis 0.04 coefficient of variation (CV) 10.38% 1st quartile 375.75 median 395.50 3rd quartile 433.50 interquartile range 57.75 mode 407.00

According to the summary statistics, the mean sale price is 404.18 (\$/ton), The range of the sale price is 175 (\$/ton) and the standard deviation is 41.96 (\$/ton).

1. The frequency table for, the average sale price, average delivery time, and average customer satisfaction for each city is given below: The graph is shown below:

 Row Labels Count of Sale price (\$/ton) Count of Customer satisfaction Count of Delivery time (minutes/ton.km) Brisbane 11 11 11 Canberra 6 6 6 Melbourne 14 14 14 Sydney 19 19 19 Grand Total 50 50 50

The graph is shown below:

According to the above frequency table and bar graph for each city. The frequency of “Sydney” city is highest which is19 and the frequency of the “Canberra” is lowest which is 6 for the sales price, customer satisfaction and delivery time.

1. The scatter diagram between the delivery time and the sales price is shown below:

The above scatterplot indicates a negative relationship between the sales price and the delivery time, as the delivery time increases the sale price decreases.

The sample correlation coefficient between the delivery time and the selling price is -0.434 which indicates a moderate negative relationship between the sales price and the delivery time.

1. The scatter diagram between the delivery time and the customer satisfaction is shown below:

The above scatterplot indicates a negative relationship between the customer satisfaction and the delivery time, as the delivery time increases the customer satisfaction decreases.

The sample correlation coefficient between the delivery time and the customer satisfaction is -0.736 which indicates a strong negative relationship between the customer satisfaction and the delivery time.

1. The scatter diagram between the sale price and the customer satisfaction is shown below:

The above scatterplot indicates a positive relationship between the customer satisfaction and the sale price, as the customer satisfaction increases the sale price increases.

The sample correlation coefficient between the customer satisfaction increases the sale price is 0.492 which indicates a moderate positive relationship between the customer satisfaction increases the sale price.

1. The scatter chart to examine the relationship between the average response time and the total number of incidents is shown below:

The above scatter chart indicates a negative relationship between the average response time and the total number of incidents, as the total number of incidents increases the average response time decreases.

The regression line is:

The slope of the regression line is  which is negative and so it depicts that average response time is expected to decrease (or increase) by 0.191 percentages as “number of incidents” increases (decreases) by one.

The average response time will be 1107 .25 when the number of incidents is zero.

1. The scatter chart to examine the relationship between the percentage of less than 15 minutes response times and the average response time is shown below:

The above scatter chart indicates a negative relationship between the percentage of less than 15 minutes response times and the average response, as the percentage of less than 15 minutes response times increases the average response time decreases.

The regression line is:

The slope of the regression line is  which is negative and so it depicts that average response time is expected to decrease (or increase) by 1145.328 percentages as “percentage of less than 15 minutes response times” increases (decreases) by one. The average response time will be 1641 when the percentage of less than 15 minutes response times is zero.

1. The frequency distributions, percent frequency distributions and intervals in a table for the number of incidents using bin size of 250 incidents is calculated as below:
 Number of incidents cumulative lower upper midpoint width frequency percent frequency percent 0.0 < 10.0 5.0 10.0 0 0.0 0 0.0 10.0 < 20.0 15.0 10.0 0 0.0 0 0.0 20.0 < 30.0 25.0 10.0 1 4.2 1 4.2 30.0 < 40.0 35.0 10.0 0 0.0 1 4.2 40.0 < 50.0 45.0 10.0 0 0.0 1 4.2 50.0 < 60.0 55.0 10.0 0 0.0 1 4.2 60.0 < 70.0 65.0 10.0 1 4.2 2 8.3 70.0 < 80.0 75.0 10.0 0 0.0 2 8.3 80.0 < 90.0 85.0 10.0 0 0.0 2 8.3 90.0 < 100.0 95.0 10.0 1 4.2 3 12.5 100.0 < 110.0 105.0 10.0 1 4.2 4 16.7 110.0 < 120.0 115.0 10.0 2 8.3 6 25.0 120.0 < 130.0 125.0 10.0 2 8.3 8 33.3 130.0 < 140.0 135.0 10.0 0 0.0 8 33.3 140.0 < 150.0 145.0 10.0 1 4.2 9 37.5 150.0 < 160.0 155.0 10.0 1 4.2 10 41.7 160.0 < 170.0 165.0 10.0 3 12.5 13 54.2 170.0 < 180.0 175.0 10.0 2 8.3 15 62.5 180.0 < 190.0 185.0 10.0 2 8.3 17 70.8 190.0 < 200.0 195.0 10.0 0 0.0 17 70.8 200.0 < 210.0 205.0 10.0 2 8.3 19 79.2 210.0 < 220.0 215.0 10.0 2 8.3 21 87.5 220.0 < 230.0 225.0 10.0 1 4.2 22 91.7 230.0 < 240.0 235.0 10.0 0 0.0 22 91.7 240.0 < 250.0 245.0 10.0 2 8.3 24 100.0

The histogram for the frequencies is shown below:

According to the obtained frequency distribution and histogram, the maximum frequency is obtained for the class interval 160-170 number of incidents.

1. The combinations of LGA categories and rating are most represented in the Ambulance Victoria data is shown below:
 Row Labels Count of Rating Borough 1 City 32 Rural City 7 Shire 39 Grand Total 79

For the LGA category “Shire” the most of the ratings are obtained which is 39.

The table for the area with average response time more than 15 minutes (900 seconds) corresponding to the rating is shown below:

 Count of Average  response time  - Seconds Column Labels Row Labels Fair Good Poor Very Good Very poor Grand Total Borough 1 1 City 3 19 10 32 Rural City 2 4 1 7 Shire 16 4 14 1 4 39 Grand Total 21 27 14 12 5 79

Thus, for the LGA categories the rating “Good” is most represented for average response time more than 15 minutes (900 seconds). The above rankings will similarly indicates about the other quarters of the year.

1. The average incidents happened in each combination of category-rating pair of areas in the data set is shown below:
 Borough City Rural City Shire Grand Total Average of Number of incidents 62 1860.3125 423.1428571 628.1025641 1101.898734

According to the above obtained Pivot table, the maximum average number of incidents is obtained for “City” and minimum average number of incidents is obtained for “Borough”.

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