PROJECT PART A
Exploratory Data Analysis

Keller Graduate School of Management
GM533: Managerial Statistics (Downers Grove, IL)

Table of Contents
I.
Introduction & Overview .................................................................................................... 3

II.
Individual Variables............................................................................................................. 4
Variable: Location................................................................................................................ 4
Variable: Income.................................................................................................................. 4
Variable: Credit Balance .................................................................................................... 5

III.
Relationships.......................................................................................................................... 6
Location and Credit Balance................................................................................................ 7
Credit Balance and Household Size .................................................................................... 8
Income and Credit Balance .................................................................................................. 8
References............................................................................................................................... 9

I. Introduction & Overview
AJ Davis is a department store chain, which has many credit customers and wants to find out more information about these customers. The total sample set of 50 credit customers is selected with data collected.

The following data were provided for analysis.
1. Location:
a. Urban
b. Suburban
c. Rural
2. Income
3. Household Size (number of people living in the household)
4. Years (the number of years that the customer has lived in the current location)
5. Credit Balance (the customer’s current credit card balance on the store's credit card)

II. Individual Variables

Five individual variables were provided for review: Location, Income, Household Size, Years, and Credit Balance. Below is a statistical analysis summarizing the key points referencing Location, Income and Credit Balance.

Variable: Location Sample Size | 50 | Mean | $43,480 | Sample Standard Deviation | $14,404.50 | Minimum | $21,000 | Maximum | $67,000 | Range | $46,000 | | | 1st quartile | $30,250 | Median | $42,000 | 3rd quartile | $54,750 | Interquartile range | $24,500 | Mode | $54,000 |

Sample Size | 50 | Mean | $43,480 | Sample Standard Deviation | $14,404.50 | Minimum | $21,000 | Maximum | $67,000 | Range | $46,000 | | | 1st quartile | $30,250 | Median | $42,000 | 3rd quartile | $54,750 | Interquartile range | $24,500 | Mode | $54,000 |

The location of AJ Davis’ customers is distributed fairly evenly between urban, suburban and rural areas. Of the total number of customer locations in the sample set, 50, 14 are located in rural, 15 in suburban and 21 in urban locations. The pie chart shows that just less than half of all AJ Davis’ customers live in urban (42%) areas, yet customers that live in rural (28%) and suburban (30%) areas are relatively evenly distributed. The rural and suburban areas combine to compromise 58% of AJ Davis’ credit customer base in which they are interested in. This should be useful information to AJ Davis as about half of their credit customers are from urban locations.

Variable: Income

The range of customer’s income is $46,000, with the highest income at $67,000 and the lowest at $21,000. The mean (average) income of a customer is $43,480. The median income is $42,000 (half way point between the 50 total incomes, 25 incomes below and 25 incomes above). The value that appears most frequent (mode) is $54,000. This information is beneficial to AJ Davis in that it gives them a snapshot of customer income information so that they will be better able to assess their customer’s ability to repay their debt, as well as help them gage if credit limits could possibly be increased.
This boxplot displays this information in a graphical format. The box represents the lower quartile of $30,250 (25% of incomes are less than this value), the median of $42,000, and the upper quartile of $54,750 (25% of incomes are greater than this value). Sample Size | 50 | Mean | $3,964.06 | Sample Standard Deviation | $924.11 | Minimum | $1,864.00 | Maximum | $5,678.00 | Range | $3,814.00 | | | 1st quartile | $3,130.50 | Median | $4,090.00 | 3rd quartile | $4,732.75 | Interquartile range | $1,602.25 | Mode | $3,890.00 |

Sample Size | 50 | Mean | $3,964.06 | Sample Standard Deviation | $924.11 | Minimum | $1,864.00 | Maximum | $5,678.00 | Range | $3,814.00 | | | 1st quartile | $3,130.50 | Median | $4,090.00 | 3rd quartile | $4,732.75 | Interquartile range | $1,602.25 | Mode | $3,890.00 |

Variable: Credit Balance

The average (mean) credit balance of AJ Davis’ customer is $3,964.06, the largest credit balance is $5,678 and smallest at $1,864, resulting in a range of $3,814. The standard deviation is $924.11. This represents that in the aggregated comparison of credit balances of AJ Davis customers (in the sample set) a relatively small variation exists from the mean of $3,964.06. The median credit balance is $4,090.00, the median often provides a clearer picture of the overall data set examined. Yet in this case being the median and mean resulted in relatively close figures (difference of only $125.94) both are representative of an “average” credit balance. This boxplot displays this information collected in a graphical format. The box represents the lower quartile of $30,250 (25% of incomes are less than this value), the median of $42,000, and the upper quartile of $54,750 (25% of incomes are greater than this value). As shown a boxplot is a valuable tool in analyzing this data as it gives a good graphical image of the concentration of the data, which is the box. They also show how far from most of the data the extreme values are, which is shown by the top and the bottom of the vertical line.

III. Relationships

Three variables were found show a strong relationship as they relate to AJ Davis’ customers. * Location and Credit Balance * Credit Balance and Size * Income and Credit Balance

Location and Credit Balance
A look at the mean credit balances by location shows that the highest average credit balance is for suburban areas, with the mean of $4,654. The second highest average credit balance is for houses located in urban areas ($4,162) and followed by rural areas ($2,928). As we previously saw the mean results and the median results of all credit customers were relatively close to one another. The median values based on location held closely to this same trend, with suburban areas exhibiting the median value ($4,820). This data begins to prove both useful and interesting in that although the suburban area holds the highest average credit balance they only account for 30% of all AJ Davis’ customers as preveiously discussed. At the same time the rural area only accounts for 28% of all AJ Davis’ customers and also has the lowest average credit balance. This data begins to show a link between location and credit balance.

Credit Balance and Size
As previously discussed the average (mean) credit balance of all AJ Davis’ customers is $3,964.06. By using this information along with the data shown on the graph to the right we can see that on average household sizes of 3 or more have a credit balance higher than the overall mean credit balance of all AJ Davis’ customers. There also appears to be a correlation between an increase in household size and an increase in credit balance.

Income and Credit Balance

A scatter plot diagram provides a graphical observation of how two different variables are related to one another. Looking at the data collected for credit balance of customers along with the data collected for income of customers, it’s easy to recognize that there is a correlation between the two variables. The linear positive slope indicates that an increase in the credit balance correlates with an increase in income.
References:

Statistics for Business and Economics 11th Edition By: McClave, Benson, and Sincich
Prentice Hall/Pearson © 2011