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Statistics for Decision Making: Luxury Car Buyers

ECON 940 – Statistics for Decision Making

PRESENTATION OF ASSIGNMENT

  1. The answer to your assignment should be in the form of a business report.
  2. Marks awarded will be based on presentation (5%) as well as the rest (90%).
  3. The report will provide you with an opportunity to demonstrate proficiency in integrating statistical software SPSS, Mintab, KaddStat, Excel/PhStat with a word processor, Word. Note that you can easily import Minitab, KaddStat, SPSS, Excel/PhStat output to Word.
  4. Your report must include:
  5. An Executive Summary (100 to 150 words). In this section you summarize the main conclusions of the report in business language. It should also describe the primary purpose of the study, the general methodology used, the significant findings of each section, as well as key general conclusions and recommendations.
  6. A Table of Contents with page numbers
  7. Business Problem as given in the question in business language.
  8. Statistical problem using the language of statistics (i.e. methods you have used to do your analysis).
  9. Analysis: This section should present statistical output and discuss the results from all the analyses conducted. Outline required steps and show necessary computer output. Clearly label tables and graphs.
  10. General Conclusion: This section should briefly review the study, summarize the inference(s) stemming from it, and highlight the evidence supporting each inference. Where appropriate, indicate the limitations of the results. The conclusions should be written in business language and in terms of the variables under discussion.
  11. Implications: bearing in mind why the study was undertaken, briefly describe the implications and consequences of the conclusions drawn. You should include your recommendations for action (based on what you have found in your study).
  12. Write clearly and precisely. A precise report is a clear report, one that is composed of unambiguous statements. The word limit is 3000 words.

Answer

Executive Summary:

The scope of the study is to analyze the data of luxury car buyers. The data set consists of type of car and details of people buying the car namely age, annual income and year of experience in education. The different tasks are executed by analyzing the data in excel. From the statistical analysis it is found that the age, annual income and education of people can affect the selection of luxury cars. The report also shows the results of test that older people with higher annual income and higher education mostly prefer Mercedes. From the results, it is recommended that marketing and sales strategies can be made in such a way to attract the target customers. Each car type buyers have some unique similarities which are explained in the report. It can also used to increase the sales by making strategies for different types of cars.

Task 1

cars purchased by different age groups

A car manufacturer creates various plans to market it. The above data points represent the cars purchased by different age groups. The visual is shown as Line chart. 

BMW car buyer’s age is in the range from 36 to 57. LEXUS car buyer’s age is in the range from 36 to 68. The buyers of the Mercedes have ages in the range from 35 to 70.

It is important to keep in mind that vehicles advertisements must reach the respective age groups.

Ages of People Buying Cars
BMWLexusMercedes
555652
414654
434853
574464
425649
414943
475550
464948
BMW Lexus Mercedes 
Mean45.21538Mean50.45714Mean51.98667
Standard Error0.381908Standard Error0.515472Standard Error0.55037
Median45Median50Median53
Mode46Mode55Mode53
Standard Deviation4.354423Standard Deviation6.099147Standard Deviation6.740628
Sample Variance18.961Sample Variance37.19959Sample Variance45.43606
Kurtosis0.04742Kurtosis0.611214Kurtosis-0.0195
Skewness0.508655Skewness0.360262Skewness-0.02894
Range21Range32Range35
Minimum36Minimum36Minimum35
Maximum57Maximum68Maximum70
Sum5878Sum7064Sum7798
Count130Count140Count150

DESCRIPTIVE STATISTICS OF BMW CARS

Minimum of 36 and maximum of 57 year old people has interest to buy BMW. The total number of BMW purchases is 130

DESCRIPTIVE STATISTICS OF LEXUS CARS

 Minimum 36 and maximum 68 years of age groups are attracted by Lexus. The total number of LEXUS purchases is 140.

DESCRIPTIVE STATISTICS OF MERCEDES CAR

Minimum 35 and maximum 70 years of age groups are attracted by Mercedes. The total number of Mercedes purchases is 150.

From the detailed statistics based on the people’s age that has higher age mostly prefer only Mercedes.

Task 2

Three different luxury cars are required to display data with annual income of buyers. Next, we need to calculate statistics with three different luxury cars with their income in dollar.

A car manufacturer produces various plans to market it. In this regard, we are investigating to find out which types of cars are purchased with buyers on annual income basis. 

Row LabelsAverage of Annual Income ($)
BMW139271.3385
Lexus154186.8571
Mercedes184423.9467
Grand Total160369.1095


Type of cars is taken on the horizontal axis has been analyzed with annual income on the vertical axis

Type of cars is taken on the horizontal axis has been analyzed with annual income on the vertical axis. The analysis shows that People earning average annual profits of 139271.3385 (dollar) buy BMW. People with an average annual income of 154186.8571 dollar buy Lexus. People with average earnings per annum of 184423.9467 dollar buy Mercedes.

 It seems to have Mercedes as a desire for higher annual income. It is important to keep in mind those vehicles advertisements should reach out to those with suitable annual income during marketing.


annual income

BMWLexusMercedes
148,066118,571161,590
191,835129,564129,017
172,689120,807194,379
159,380159,132226,016
138,269120,165153,589
166,091160,062275,299
105,033200,609135,562
176,274170,884211,308

bmw lexus mercedes 






Mean139271.3Mean154186.9Mean184423.9
Standard Error2907.846Standard Error2556.425Standard Error3845.333
Median138512Median154492Median186070
Mode109568Mode179617Mode161590
Standard Deviation33154.54Standard Deviation30248.02Standard Deviation47095.52
Sample Variance1.1E+09Sample Variance9.15E+08Sample Variance2.22E+09
Kurtosis-0.22439Kurtosis0.963641Kurtosis0.987178
Skewness-0.03855Skewness0.693685Skewness0.273966
Range170652Range152065Range284882
Minimum46068Minimum96069Minimum49941
Maximum216720Maximum248134Maximum334823
Sum18105274Sum21586160Sum27663592
Count130Count140Count150

DESCRIPTIVE STATISTICS FOR BMW CAR

People prefer BMW who got minimum 46068 dollars and a maximum of 216720 dollar annually. The total number of BMW purchases is 130

Mean:

The middle trend is the mean or average commonly used method. To calculate the mean value you have to do addition of all the values and divide by the number of values.

By using average annual income of buyers and BMW the mean value for buyer’s average annual income is 139271.3 dollar.

Median: 

By using average annual income of buyers and BMW, median value for buyer’s average annual income is 138512 dollar.

Mode:

The most frequently occurring value in a set of scores. The most frequently occurring value is known as mode.

The most frequently occurring value in the given data set for BMW is 109568 dollar.

Note:

In the same set of ages, we have the mean, median and mode three different values for 139271.3138512and 109568 (dollars) respectively. If the distribution is really normal (ie in the form of a bell), the mean, median and mode are all equal to each other.

DESCRIPTIVE STATISTICS FOR LEXUS CAR

People who got minimum 96069 dollar and maximum 248134 dollar yearly income attracted by Lexus. Total number of Lexus buyers is 140.

Mean:

By using average annual income of buyers and Lexus the mean value for buyer’s average annual income is 154186.9 dollar 

Median: 

By using average annual income of buyers and Lexus the median value for buyer’s average annual income is 154492 dollar

Mode:

The most frequently occurring value in a set of scores. To determine the system, sort scores as shown above, then count each. The most frequently occurring value is known as mode.

The most frequently occurring value in the given data set is 179617 dollar.

Note:

In the same set of ages, we have the mean, median and mode three different values for 154186.9154492179617 (dollar) respectively. If the distribution is really normal (ie in the form of a bell), the mean, median and mode are all equal to each other.

DESCRIPTIVE STATISTICS FOR MERCEDES CAR

People who got minimum 49941 dollar and maximum 334823 dollar yearly prefer only Mercedes. The total number of Mercedes purchases is 150.

Mean:

By using average annual income of buyers and Mercedes the mean value for buyer’s average annual income is 184423.9 dollar.

Median: 

The exact middle value of the set is known as median. List all scores in a way of numerical order to calculate the average, then find the centre score in the sample.

By using average annual income of buyers and Mercedes the median value for buyer’s average annual income is 186070dollar. 

Mode:

The most frequently occurring value in a set of scores. To determine the system, sort scores as shown above, then count each. The most frequently occurring value is known as mode.

The most frequently occurring value in the given data set is 161590 dollar.

Note:

In the same set of ages, we have the mean, median and mode three different values for 184423.9186070and 161590 (dollars) respectively. If the distribution is really normal (ie in the form of a bell), the mean, median and mode are all equal to each other.

Task 3

Three different luxury cars have to display data with the years of education of buyers. Next, we need to calculate statistics with the years of education of buyers of three different luxury cars.

Row LabelsAverage of Education (Years)
BMW15.83076923
Lexus15.8
Mercedes17.29333333
Grand Total16.34285714

Type of cars on The horizontal axis which is analyzed with an average year of education on a vertical axis

A car manufacturer produces various plans to market it. Studies have been made to find out which types of cars they have with year of education. Let's see in detail the data analysis on the top. Type of cars on The horizontal axis which is analyzed with an average year of education on a vertical axis. 

The year of education of 15.83076923 people buy BMW. 

An average year of education 15.8 people buys Lexus. 

The year of education of education17.29333333 people are getting Mercedes.

It seems that Mercedes as a desire for higher year's education

It is important to keep in mind that vehicles must be reached to those who have a suitable year of education in marketing.

Education (Years)  
BMWLexusMercedes
181520
161214
171818
171617
111918
171717
151417
151915


bmw lexus mercedes 
Mean15.83076923Mean15.8Mean17.29333
Standard Error0.160922527Standard Error0.204069593Standard Error0.142067
Median16Median16Median17
Mode16Mode16Mode17
Standard Deviation1.83479911Standard Deviation2.414583986Standard Deviation1.739963
Sample Variance3.366487776Sample Variance5.830215827Sample Variance3.027472
Kurtosis-0.172883895Kurtosis-0.977282698Kurtosis0.039633
Skewness-0.434503723Skewness0.169719918Skewness0.081676
Range8Range9Range9
Minimum11Minimum12Minimum13
Maximum19Maximum21Maximum22
Sum2058Sum2212Sum2594
Count130Count140Count150

DESCRIPTIVE STATISTICS OF BMW CAR

People whose preference for BMW has minimum 11 and maximum of 19 years of education. The total number of BMW purchases is 130

Mean:

The middle trend is the mean or average commonly used method. To calculate the mean value you have to do addition of all the values and divide by the number of values.

By using average annual income of buyers and type of three different cars mean value for buyers average education is 15.83076923,

Median: 

The exact middle value of the set is known as median. List all scores in a way of numerical order to calculate the average, then find the centre score in the sample.

By using average annual income of buyers and type of three different cars median value for buyer’s average education are 16.

Mode:

The most frequently occurring value in a set of scores. To determine the system, sort scores as shown above, then count each. The most frequently occurring value is known as mode.

The most frequently occurring value in the given data set is 16.

Note:

In the same set of ages, we have the mean, median and mode three different values for 15.83076923,, 1616 (average age) respectively. If the distribution is really normal (ie in the form of a bell), the mean, median and mode are all equal to each other.

DESCRIPTIVE STATISTICS OF LEXUS CAR

People who has minimum 12 and maximum 21year of educators are attracted by Lexus. Total number of Lexus buyers is 140

Mean:

The middle trend is the mean or average commonly used method. To calculate the mean value you have to do addition of all the values and divide by the number of values.

By using average annual income of buyers and type of three different cars mean value for buyers average education is 15.8

Median: 

The exact middle value of the set is known as median. List all scores in a way of numerical order to calculate the average, then find the centre score in the sample.

By using average annual income of buyers and type of three different cars median value for buyer’s average education are 16.

Mode:

The most frequently occurring value in a set of scores. To determine the system, sort scores as shown above, then count each. The most frequently occurring value is known as mode.

The most frequently occurring value in the given data set is 16.

Note:

In the same set of ages, we have the mean, median and mode three different values for 15.8,, 1616(average age)  respectively. If the distribution is really normal (ie in the form of a bell), the mean, median and mode are all equal to each other.

DESCRIPTIVE STATISTICS OF MERCEDES CAR

Minimum 13 and maximum 22 years of education prefer Mercedes. The total number of Mercedes purchases is 150

This quality analysis can make sense of Mercedes as a desire for people with higher years of education

Mean:

The middle trend is the mean or average commonly used method. To calculate the mean value you have to do addition of all the values and divide by the number of values.

By using average annual income of buyers and type of three different cars mean value for buyers education is 17.29333(average age)

Median: 

The exact middle value of the set is known as median. List all scores in a way of numerical order to calculate the average, then find the centre score in the sample.

By using average annual income of buyers and type of three different cars median value for buyer’s education is 17(average age)

Mode:

The most frequently occurring value in a set of scores. To determine the system, sort scores as shown above, then count each. The most frequently occurring value is known as mode.

The most frequently occurring value in the given data set is 17.

Note:

In the same set of ages, we have the mean, median and mode three different values for 17.29333,,17, 17(average age)  respectively. If the distribution is really normal (ie in the form of a bell), the mean, median and mode are all equal to each other.

Task 4

The scope of the task is to test the belief that there is no significant difference of the average ages of the buyers of three different luxury cars

Row LabelsAverage of Age (Years)
BMW45.21538462
Lexus50.45714286
Mercedes51.98666667
Grand Total49.38095238


Type of cars is taken on the horizontal axis which is analysed with average age of buyers on vertical axis

Type of cars is taken on the horizontal axis which is analysed with average age of buyers on vertical axis.

Bar chart will created by using excel with help of the given data. 

The people of average age 45.21538462 have bought BMW.

The people of average age 50.45714286 have bought LEXUS. 

The People of average age 51.98666667 have bought Mercedes.

This means that Mercedes is attracted by more aged people. This decision is made clear that there is considerable difference in age for buying cars.

Task 5

In this task we will discuss about the belief that that there is no significant difference in mean household incomes of the three different luxury cars.

Row LabelsAverage of Annual Income ($)
BMW139271.3385
Lexus154186.8571
Mercedes184423.9467
Grand Total160369.1095



Type of cars is taken on the horizontal axis which is analysed with average annual income of buyers on vertical axis.

Bar chart is created by using excel with help of the given data. 

People of An average annual income 139271.3385 dollar have bought BMW. 

People of An average of annual income 154186.8571 dollar have bought LEXUS. 

People of An Average of annual income 184423.9467 dollar have bought Mercedes.

This makes us feel Mercedes as the choice of most annual income. This decision is made clear that there is a substantial amount of annual income on buying cars

Task 6

In this task we will discuss about the belief that that there is no significant difference in mean household incomes of the three different luxury cars.


Row LabelsAverage of Education (Years)
BMW15.83076923
Lexus15.8
Mercedes17.29333333
Grand Total16.34285714


Type of cars are taken on the horizontal axis which is analysed with Average of Education (Years) of buyers on vertical axis

Type of cars are taken on the horizontal axis which is analysed with Average of Education (Years) of buyers on vertical axis.

Bar chart will created by using excel with help of the given data. 

People of An Average of Education (Years) 15.83076923 have bought BMW. 

People of An Average of Education (Years) 15.8 have bought LEXUS. 

People of An Average of Education (Years) 17.29333333 have bought Mercedes.

This makes us feel Mercedes as the choice of higher education (year) people. This decision is made clear by considering a substantial amount of years of education in buying luxury cars.

Task 7

In this task we will discuss about the belief “Some other car dealers claim that older people with higher household income and more years of education prefer Mercedes to BMW or Lexus”.


Values
Row LabelsAverage of Annual Income ($)Average of Education (Years)
7018473517
Mercedes18473517
6815313812
Lexus15313812
6613455614
Lexus13455614
6418693617
Mercedes18693617
6319566315.5
Lexus17160513
Mercedes21972118
62178344.516
Lexus17061915
Mercedes18607017
6113741219.5
Lexus11427617
Mercedes16054822
6013879717
Mercedes13879717

Above table contains type of cars with respect to age, average annual income, and average education details of the buyers

It will clearly show when the ages of buyers’ increases BMW car lose their place. It means that people with higher age and higher annual income people do not prefer BMW.

Our problem is some other car dealer’s claim that older people with higher household income and more years of education prefer Mercedes to BMW or Lexus. It may be false because highest education of people with low level income also selecting Lexus.

For example ,in this table take that 70 aged customer their annual income is 184735 dollar  but their years of education is low when compared with others they choose Mercedes as favourite car.

May be annual income of the customer and age will affect the choosing of their favourite car but year of education doesn’t matter when choose a favourite car.

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