Final Assingment of QTM.
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Transcript of Final Assingment of QTM.
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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