MATH533: Applied Managerial Statistics

Kunal Desai

D40301460

Kunalad@yahoo.com

Professor – Nathaniel Litton

Course project – part A

I. Introduction.

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)

3. Size (Household size)

4. Years (the number of years that the customer has lived in the current location)

5. Credit balance (the customers current credit balance on the store’s credit card, in $)

II. Individual variables.

1. Size

Tally for Discrete Variables: Size

Variable Mean StDev Variance Minimum Q1 Median Q3 Maximum RangeSize 4.500 2.525 6.378 1.000 2.000 4.500 7.000 8.000 7.000

N forVariable Mode ModeSize 1, 8 8

Category 1 – 16%

Category 2 – 14%

Category 3 - 12%

Category 4 – 8%

Category 5 – 8%

Category 6 – 12%

Category 7 – 14%

Category 8 – 16%

Interpretation: Look at the table and the Pie chart above, we can see the Sizes of AJ Davis’

customers is distributed in 8 Categories. The above Pie chart helps us to know the different

sizes. Range is 7 where as mean and median are same that’s 4.500.

2. Income.

Descriptive Statistics: Income ($1000)

Variable Mean StDev Variance Minimum Q1 Median Q3 MaximumIncome ($1,000) 46.02 13.88 192.75 25.00 33.00 44.50 57.25 74.00

N forVariable Range Mode ModeIncome ($1,000) 49.00 30, 33, 54, 57 3

Interpretation: Based on the table and histogram, we have some comments as follow.

The range of customer’s income is $49,000, with the highest income at $74,000 and the lowest at

$25,000.   The mean (average) income of a customer is $46,020. The median income is $44,050.

Because the median is less than the mean, distribution is skewed to the right. This means the

bigger portion of customers have an income under the rest of customers. However, this

difference is not much.

3. Credit balance

Descriptive Statistics: Credit Balance($)

Variable Mean StDev Variance Minimum Q1 Median Q3 MaximumCredit Balance($) 4153 932 868430 2047 3292 4273 4931 5861

N forVariable Range Mode ModeCredit Balance($) 3814 4073 2

Interpretation: The range of customer’s credit balance is $3814, with the highest credit balance at

$5861 and the lowest at $2047. The mean (average) credit balance of a customer is $4153. The

median credit balance is $4273. We can see distribution is skewed to the left because the median

is more than the mean. Look at the histogram, we can see that a bigger portion of cardholders

carries an approximate $4000 balance. This means that a greater number of customers have a

credit balance in this range.

III. Relationships

1. Locations and Income

Descriptive Statistics: Income ($1000)

Variable Location Mean StDev Variance Minimum Q1 MedianIncome ($1,000) Rural 37.54 8.07 65.10 25.00 31.50 36.00 Suburban 47.27 15.15 229.64 25.00 32.00 46.00 Urban 50.18 13.99 195.68 27.00 38.75 54.00

N forVariable Location Q3 Maximum Range Mode ModeIncome ($1,000) Rural 45.00 53.00 28.00 33 3 Suburban 64.00 69.00 44.00 32, 57 2 Urban 61.00 74.00 47.00 54 3

Look at the above table we can see the difference in income regarding the location of customers.

The means indicate the average income of each area the Rural, Suburban and Urban. We can also

observe the difference in average income of the three areas and suburban area has the biggest

income with $69,000. In rural and urban areas, customers have the highest income with $53,000

and 74,000. Therefore, AJ DAVIS should target customers in these areas.

2. Locations and Size

Tabulated statistics: Location, Size

TotalVariable Location Count Mean StDev Variance Minimum Q1 MedianSize Rural 13 6.692 1.251 1.564 4.000 6.000 7.000 Suburban 15 4.600 2.694 7.257 1.000 2.000 4.000 Urban 22 3.136 2.054 4.219 1.000 1.000 2.500

N forVariable Location Q3 Maximum Range Mode ModeSize Rural 8.000 8.000 4.000 7, 8 4 Suburban 8.000 8.000 7.000 8 4 Urban 5.000 7.000 6.000 1 6

Firstly, we can see that a majority of customers lives in urban area, the second is suburban area

and then rural area.

3. Credit balance and size.

Descriptive Statistics: Credit Balance ($)

Variable Size Count Mean StDev Variance Minimum Q1Credit Balance ($) 1 8 3616 498 247718 2631 3249 2 7 4221.4 108.0 11666.3 4073.0 4082.0 3 6 4573 283 80281 4354 4363 4 4 3962 1308 1711244 2047 2635 5 4 4297 1115 1243965 2660 3144 6 6 3916 1237 1531338 2697 2749 7 7 4157 1218 1482725 3104 3178 8 8 4516 1190 1415970 3257 3314

N forVariable Size Median Q3 Maximum Range Mode ModeCredit Balance($) 1 3788 4015 4073 1442 * 0 2 4253.0 4310.0 4340.0 267.0 * 0 3 4424 4931 4947 593 * 0

4 4400 4853 5003 2956 * 0 5 4691 5058 5148 2488 * 0 6 3901 5063 5220 2523 * 0 7 3250 5528 5553 2449 * 0 8 4560 5688 5861 2604 * 0

From this table, we can see that the households containing 5 people have the highest credit

balance of $4691, the second is household size of 8 and then is household size of 3. And the

lowest credit balance is 3250.

IV. Conclusion.

Based on the statistics and the analysis above, we can understand more clearly about the

customers of AJ DAVIS. We already know who customers are, where they are, how their family

is about… And from those, we can determine what we should do on the future to attract more

customers.

In short, statistics is useful for us in business because it allow us to analyze and determine the future tendency effectively.