Final Assingment of QTM.

5/28/2018 Final Assingment of QTM.

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2011University ofManagement &technology

Waiza WaheedSaad SaleemFarah Zaidi

[STATISTICAL TECHNIQUES IN BUSINESS & ECONOMICS]In statistical techniques in business and economics we study how to describe , display and

explore data using different measure of central tendency and measure of dispersions, and alsowe see how to represent data in graphs. In this assignment we solve three case studies by usingthese measures.


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Subject:Statistical Techniques in Business & Economics

Assignment: Case studies

Submitted To:Mr.Umer Ayub

Submitted By:

Waiza Waheed 104732-114

Saad Saleem 104732-

Farah Zaidi 104732-

Program: MBA (P)3

Section: A

School of Business and Economics

UNIVERSITY OF MANAGEMENT &

TECHNOLOGY


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Case Study (A). Century Bank

Solution:

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

x1 x2 x3 x4 x5 x6

1756 13 4 0 1 2

748 9 2 1 0 1

1501 10 1 0 0 1

1831 10 4 0 1 3

1622 14 6 0 1 4

1886 17 3 0 1 1

740 6 3 0 0 3

1593 10 8 1 0 1

1169 6 4 0 0 4

2125 18 6 0 0 2

1554 12 6 1 0 3

1474 12 7 1 0 1

1913 6 5 0 0 1

1218 10 3 1 0 1

1006 12 4 0 0 1

2215 20 3 1 0 4

137 7 2 0 0 3

167 5 4 0 0 4

343 7 2 0 0 1

2557 20 7 1 0 4

2276 15 4 1 0 3

1494 11 2 0 1 1

2144 17 3 0 0 3

1995 10 7 0 0 2

1053 8 4 1 0 3

1526 8 4 0 1 2


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1120 8 6 1 0 3

1838 7 5 1 1 3

1746 11 2 0 0 2

1616 10 4 1 1 2

1958 6 2 1 0 2

634 2 7 1 0 4

580 4 1 0 0 1

1320 4 5 1 0 1

1675 6 7 1 0 2

789 8 4 0 0 4

1735 12 7 0 1 3

1784 11 5 0 0 1

1326 16 8 0 0 3

2051 14 4 1 0 4

1044 7 5 1 0 11885 10 6 1 1 2

1790 11 4 0 1 3

765 4 3 0 0 4

1645 6 9 0 1 4

32 2 0 0 0 3

1266 11 7 0 0 4

890 7 1 0 1 1

2204 14 5 0 0 2

2409 16 8 0 0 2

1338 14 4 1 0 22076 12 5 1 0 2

1708 13 3 1 0 1

2138 18 5 0 1 4

2375 12 4 0 0 2

1455 9 5 1 1 3

1487 8 4 1 0 4

1125 6 4 1 0 2

1989 12 3 0 1 2

2156 14 5 1 0 2

Total 618 265 26 16 144

REQUIREMENT:

1) Develop a graph or table that portrays the checking balances. What is the balanceof 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?


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2) Mean & Median of four branches compare the mean & the median of the fourbranches. 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 thirdQuartile (Q1 & Q3).Determine the coefficient of skewness and indicate what itshows.

Q1. The no of ATM transaction in the last

month

= 618 no of transactions in the last month

Q2. 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 thefacility 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:

X2 X3 X4 X5

Mean 10.3 4.416666667 0.433333333 0.266666667

Median 10 4 0 0

(C).

I. Range and standard deviation:X2 X3 X4 X5 X6

RANGE 18 9 1 1 3

S.D 4.295444966 1.976914791 0.499717434 0.445948491 1.107753873


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I. Quartiles:

X2 X3 X4 X5 X6

Q1 15.25 15.25 15.25 15.25 15.25

Q3 45.75 45.75 45.75 45.75 45.75

II. Coefficient of Skewness.

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

X2 X3 X4 X5 X6

Sk 0.209 0.252 2.603 1.75038 1.083

Q1=n+1(25/100)

=60+1(25/100)

=15.25Q3=n+1(75/100)

=60+1(75/100)

=45.75


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

SolutionRequirements of the case:

a) Cumulative Frequency Distributionb) Several measures of locationc) Draw Chart (Bar char, Histogram, Line Chart)d) Quartilee) Summarize the Situation

a)Cumulative Frequency Distribution Table:

YearlySalary

Women(F)

Men(F)

MidPoint

FM ofWomen

FM ofMen

C.F(women)

C.F(Men)

less than30

2 0 25 50 25 2 0

30-40 3 1 35 105 35 5 1

40-50 17 4 45 765 180 22 5

50-60 17 24 55 935 1320 39 2960-70 8 21 65 520 1365 47 50

70-80 3 7 75 225 16875 50 57

80 or more 0 3 85 0 0 50 60

Total 50 60 2600 19800


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b)Several measures of locationSeveral measures of location are mean & median

Mean of Womens salary:Mean=FM/n

= 2600/7

Mean =371.43 Answer

Median of womens salary:Median=Central value of Data

So,

Median=17 Answer

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

Mean=2828.57 Answer

Median of Mens salary:Median= Central Value

So,

Median=24 Answer


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

23

17 17

8

3

001

4

24

21

7

3

0

5

10

15

20

25

30

less then

30

30-40 40-50 50-60 60-70 70-80 80 or

more

Frequency

Yearly Salary

Line Chart

Women

Men

23

17 17

8

3

001

4

24

21

7

3

0

5

10

15

20

25

30

less then

30

30-40 40-50 50-60 60-70 70-80 80 or

more

F

requency

Yearly Salary

Bar Chart

Women

Men


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Histogram of WOMEN SALRAY:

Histogram of MEN SALARY:

0 14

2421

730

5

10

15

20

25

30

Less

than 30

30 up to

40

40 up to

50

50 up to

60

60 up to

70

70 up to

80

80 or

more

Frequency

Yearly Salary

Histogram

Men

2 3

17 17

8

300

5

10

15

20

Less

than 30

30 up

to 40

40 up

to 50

50 up

to 60

60 up

to 70

70 up

to 80

80 or

more

Frequency

Yearly Salary

Histogram

Women


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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


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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 groups

Group #1: Commissions earned by sale representatives calling

on Athletic Department.

First arranged the data

No. of Salesrepresentative

XCommissions

Earned

(x-xbar)^2

1 4 669573.98

2 7 664673.33

3 13 654926.03

4 39 613519.73

5 69 567423.23

6 87 540629.33

7 149 453299.23

8 159 439933.73

9 175 418964.93

10 249 328644.23

11 252 325213.58

12 278 296235.2813 299 273816.73

14 354 219281.48

15 357 216480.83

16 392 185136.58

17 416 165059.38

18 427 156242.33

19 434 150757.48

20 526 87778.876

21 527 87187.326

22 557 70370.826

23 579 59182.726


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24 615 42962.926

25 635 35071.926

26 680 20242.176

27 883 3687.5256

28 1105 79933.42629 1106 80499.876

30 1168 119525.78

31 1187 133024.33

32 1602 607971.08

33 1604 611093.98

34 1676 728846.38

35 1683 740847.53

36 1738 838552.28

37 2197 1889868.8

38 2321 2246176.639 3140 5371849.2

40 3202 5663091.1

Total 32891 26857576

Central Tendency:

As we know that the measures of central tendency are mean , median and

mode.

So,

Mean=x/n

=32891/40

Mean= 822.275

And

Median= central value

=526+527/2Median=526.5

And

Mode= repeating value

We have no repeating value in this group #1

So,

Mode=N/A


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Measures of Dispersion of Group #1

We know that the measures of dispersions are range, variance, quartile,

deciles, and percentiles

Range= largest value- smallest value

=3202-4

Range=3198

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

=26857576/40-1

Variance=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


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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


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Group#2: Commission earned by sale representatives calling on large

retailers ($)

No. of salerepresentative

X (x-Xbar)^2

1 12 1096627.84

2 681 143035.24

3 719 115736.04

4 754 93147.04

5 758 90721.44

6 807 63604.84

7 850 43764.64

8 870 35796.649 886 29998.24

10 886 29998.24

11 899 25664.04

12 918 19937.44

13 934 15675.04

14 944 13271.04

15 1066 46.24

16 1083 566.44

17 1116 3226.24

18 1206 21550.24

19 1213 23654.44

20 1244 34151.04

21 1255 38337.64

22 1262 41127.84

23 1291 53731.24

24 1294 55131.04

25 1313 64414.44

26 1315 65433.64

27 1338 77729.4428 1448 151165.44

29 1556 246810.24

30 1858 638081.44

Total 31776 3332134.8


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Central Tendency:

Mean=x/n

=31776/30

Mean=1059.2

& Median= central value

So,

Median=1074.5

And Mode=Repeating ValueSo,

Mode=886

Measures of Dispersion of Group #2

Range= largest value- smallest value=1858-12

Range=1846

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

= 3332134.8/30-1

variance=114901.2

Final Assingment of QTM.

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