Statistical techniques in business & economics

Case Study (A). Century BankSolution:

x1= Account Balance in $

x2=Number of ATM transaction in the month

x3=Number of other Bank services used

x4=Has a debit card( 1=Yes, 0=No )

x5=Receives interest on the account ( 1=Yes, 0=No )

x6=City where banking is done

x1x2x3x4x5x6

1756134012

74892101

1501101001

1831104013

1622146014

1886173011

74063003

1593108101

116964004

2125186002

1554126103

1474127101

191365001

1218103101

1006124001

2215203104

13772003

16754004

34372001

2557207104

2276154103

1494112011

2144173003

1995107002

105384103

152684012

112086103

183875113

1746112002

1616104112

195862102

63427104

58041001

132045101

167567102

78984004

1735127013

1784115001

1326168003

2051144104

104475101

1885106112

1790114013

76543004

164569014

3220003

1266117004

89071011

2204145002

2409168002

1338144102

2076125102

1708133101

2138185014

2375124002

145595113

148784104

112564102

1989123012

2156145102

Total6182652616144

REQUIREMENT:1) Develop a graph or table that portrays the checking balances. What is the balance of a typical customer? Do many customers have more than $2000 in their accounts? Does it appear that there is a difference in the distribution of the accounts among the four branches? Around what value do the account balances tend to cluster?

2) Mean & Median of four branches compare the mean & the median of the four branches. Is there a difference among the branches? Explain the difference between the mean and the median in your report.3) Range and standard deviation of the checking account balances. First and third Quartile (Q1 & Q3).Determine the coefficient of skewness and indicate what it shows.

Q1. The no of ATM transaction in the last month

= 618 no of transactions in the last monthQ2. The no of other bank services? = 265 no of other bank services

Q3. Whether the customer has a debit card?

= 26 peoples have the facility of debt card and remaining 34 peoples have not the facility of debt card

Q4. Whether or not interest is paid on the checking account? = 16 peoples have paid interest on checking account and 64 peoples are not paid interest on checking account.

(2). Mean & median of four branches:X2X3X4X5

Mean10.34.4166666670.4333333330.266666667

Median10400

(C).I. Range and standard deviation:X2X3X4X5X6

RANGE189113

S.D4.295444966

1.976914791

0.499717434

0.445948491

1.107753873

I. Quartiles:

Q1=n+1(25/100) =60+1(25/100) =15.25Q3=n+1(75/100) =60+1(75/100) =45.75

X2X3X4X5X6

Q115.2515.2515.2515.2515.25

Q345.7545.7545.7545.7545.75

II. Coefficient of Skewness.

SK=3(X-bar-Median)/s.dX2X3X4X5X6

Sk0.2090.2522.6031.750381.083

Case study (B). Wildcat Plumbing Supply, Inc.: Do we Have Gender Differences?

Solution: Requirements of the case:a) Cumulative Frequency Distributionb) Several measures of locationc) Draw Chart (Bar char, Histogram, Line Chart)d) Quartile e) Summarize the Situation

a) Cumulative Frequency Distribution Table:

Yearly SalaryWomen (F)Men (F)Mid PointFM of WomenFM of MenC.F(women)C.F(Men)

less than 302025502520

30-4031351053551

40-5017445765180225

50-6017245593513203929

60-708216552013654750

70-803775225168755057

80 or more0385005060

Total5060260019800

b) Several measures of location

Several measures of location are mean & median

Mean of Womens salary:Mean=FM/n = 2600/7Mean =371.43 Answer

Median of womens salary:Median=Central value of DataSo,Median=17 Answer

Mean of Mens salary:Mean=FM/n=19800/7Mean=2828.57 Answer

Median of Mens salary: Median= Central ValueSo,Median=24 Answer

C) Draw Chart (Bar char, Histogram, Line Chart)

Histogram of WOMEN SALRAY:

Histogram of MEN SALARY:

d) Quartiles:

Q1=n+1(25/100) =7+1(25/100)

Q1=2 Answer

Q2=n+1(50/100) =7+1(50/100)

Q2=4 Answer

Q3=n+1(75/100)=7+1(75/100)

Q3=6 Answer

Case (C). Kimble Products: Is there a difference in the commissions?

Solution:

Requirement of the case:

1. Write a brief report?2. Central tendency and dispersion of the two groupsGroup #1: Commissions earned by sale representatives calling on Athletic Department.

First arranged the data

No. of SalesrepresentativeXCommissions Earned(x-xbar)^2

14669573.98

27664673.33

313654926.03

439613519.73

569567423.23

687540629.33

7149453299.23

8159439933.73

9175418964.93

10249328644.23

11252325213.58

12278296235.28

13299273816.73

14354219281.48

15357216480.83

16392185136.58

17416165059.38

18427156242.33

19434150757.48

2052687778.876

2152787187.326

2255770370.826

2357959182.726

2461542962.926

2563535071.926

2668020242.176

278833687.5256

28110579933.426

29110680499.876

301168119525.78

311187133024.33

321602607971.08

331604611093.98

341676728846.38

351683740847.53

361738838552.28

3721971889868.8

3823212246176.6

3931405371849.2

4032025663091.1

Total3289126857576

Central Tendency:As we know that the measures of central tendency are mean , median and mode.

So,Mean=x/n =32891/40Mean= 822.275

And Median= central value =526+527/2Median=526.5

And Mode= repeating valueWe have no repeating value in this group #1So,Mode=N/A

Measures of Dispersion of Group #1We know that the measures of dispersions are range, variance, quartile, deciles, and percentilesRange= largest value- smallest value =3202-4Range=3198

Variance=(x-Xbar)2 /n+1 =26857576/40-1Variance=688655.8

Quartiles:Q1 =n+1(25/100 =40+1(25/100)Q1=10.25

Q2=n+1(50/100) =40+1(50/100)Q2=20.5

Q3=n+1(75/100)=40+1(75/100)Q3=30.75

Percentile:L p=n+1(P/100)=40+1(40/100)L p =16.4

Deciles:D1=n+1(10/100) =40+1(10/100)D1=4.1

D2=n+1(30/100)=40+1(30/100)D2=12.3

D3=n+1(90/100)=40+1(90/100)D3=36.9

Group#2: Commission earned by sale representatives calling on large retailers ($)

No. of sale representativeX(x-Xbar)^2

1121096627.84

2681143035.24

3719115736.04

475493147.04

575890721.44

680763604.84

785043764.64

887035796.64

988629998.24

1088629998.24

1189925664.04

1291819937.44

1393415675.04

1494413271.04

15106646.24

161083566.44

1711163226.24

18120621550.24

19121323654.44

20124434151.04

21125538337.64

22126241127.84

23129153731.24

24129455131.04

25131364414.44

26131565433.64

27133877729.44

281448151165.44

291556246810.24

301858638081.44

Total317763332134.8

Central Tendency:

Mean=x/n =31776/30Mean=1059.2

& Median= central valueSo,Median= 1074.5

And Mode=Repeating ValueSo,Mode=886

Measures of Dispersion of Group #2Range= largest value- smallest value =1858-12Range= 1846

Variance=(x-Xbar)2 /n+1 = 3332134.8/30-1variance=114901.2

Chart12

Sheet1Case B: Wildcat Plumbing SupplyYearly Salary($000)WomenMenCum.Fre of WomenCum.Fre of MenLess than 30202030 up to 40315140 up to 5017422550 up to 601724392960 up to 70821475070 up to 8037505780 or more035060

Sheet2

Sheet3