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MATH533

Given:
AJ DAVIS is a department store chain, which has many credit customers and wants to find out more information about these customers. A sample of 50 credit customers is selected with data collected on the following five variables: 1. LOCATION (Rural, Urban, Suburban) 2. INCOME (in $1,000's – be careful with this) 3. SIZE (Household Size, meaning 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 customers current credit card balance on the store's credit card, in $).
Each variable was individually considered.
Location: A categorical variable, with 3 subcategories, which are; Urban, Suburban and Rural. The frequency distribution and Bar chart are given as follows: Frequency Distribution: | | Location | Frequency | | Urban | 22 | | Suburban | 15 | | Rural | 13 | | | | |

From the frequency distribution and bar chart, it is clear that the maximum number of customers belongs to the urban sub-category (44%), followed by those in the suburban sub-category (30%). Only 26% of the customers belong to the rural sub-category.
The next variable considered is Size. It is a quantitative variable. The measures of central tendency, variation and other descriptive statistics have been calculated for this variable and are shown below:

Frequency Table | Value | Frequency | Frequency % | 1 | 8 | 16.00 | 2 | 7 | 14.00 | 3 | 6 | 12.00 | 4 | 4 | 8.00 | 5 | 4 | 8.00 | 6 | 6 | 12.00 | 7 | 7 | 14.00 | 8 | 8 | 16.00 |

Descriptive Statistics: | Size | Mean | 4.5 | Median | 4.5 | Mode | 1,8 | Standard Deviation | 2.525 | Sample Variance | 6.378 | Range | 7 | Minimum | 1 | Maximum | 8 | Sum | 225 | Count | 50 |

The mean household size of the customers is given as 4.5. The median of the data is 4.5 and the mode is 1,8. The standard deviation is given approximately as 2.525. Maximum number of customers has a household size of 8 as is evident from the frequency distribution and the bar graph.

The last individual variable considered was the Credit Balance. It is a quantitative variable. The measures of central tendency, variation and other descriptive statistics have been calculated for this variable and are given as follows: Descriptive Statistics: | Credit Balance($) | Mean | 4153.46 | Median | 4273 | Mode | 4073 | Standard Deviation | 931.8958 | Sample Variance | 868429.84 | Range | 3954 | Minimum | 2047 | Maximum | 5861 | Sum | 2076773 | Count | 50 | Relative Frequency Distribution: | Credit Balance ($) | Frequency | Relative Frequency | 2000-3000 | 6 | 12% | 3000-4000 | 13 | 26% | 4000-5000 | 20 | 40% | 5000-6000 | 11 | 22% |

The mean credit balance of the customers is given as $4,153.46. The standard deviation is given approximately as 931.8958. The credit balance of the customers is more or less normally distributed with the peak of the bell shaped distribution lying in the range $4000 - $5000. Thus, maximum number of customers has a credit balance within this range.
The relationship between the variables Income and Size is illustrated in the following scatter plot:

It is clear from the scatter plot, there is no definite relationship or association between the two variables. There is no specific pattern.
The relationship between the variables Income and Credit Balance is illustrated in the following scatter plot:

It is clear from the scatter plot, there is a relationship between the two variables. The variables Income and Credit Balance exhibit a linear positive relationship.If Income increases, Credit Balance also increases or vice versa.
The relationship between the variables Years and Credit Balance is illustrated in the following scatter plot:

It is clear from the scatter plot, the two listed variables do not show a relationship. There is no significant correlation among the variables Years and Credit Balance.
I can conclude that some of the variables such as Income are strongly conclusive of the Credit Balance of the customers in the department store.

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