Assignment # 1

Mohammad Arfan Akram

Roll .#. Ex/MBA-Spr-12-012
Semester # 1 (EMBA)

Solution (B) : Median

Solution (A) : Mean

Sr.#.

Rates for hotel

room

US Cities

Sr.#.

US Cities

Solution (C) : Mode

Rates for
hotel room

Atlanta

163

Denver

120

Boston

177

Dallas

123

Chicago

166

Minneapolis

125

Cleveland

126

Cleveland

126

Pittsburgh

134

Dallas

123

Denver

120

Phoenix

139

Detroit

144

Detroit

144

Houston

173

St. Louis

145

Los Angeles

160

Orlando

146

10

Miami

192

10

Los Angeles

160

11

Minneapolis

125

11

Seattle

162

12

New Orleans

167

12

Atlanta

163

13

New York

245

13

Chicago

166

14

Orlando

146

14

New Orleans

167

15

Phoenix

139

15

San Francisco

167

16

Pittsburgh

134

16

Houston

173

17

San Francisco

167

17

Boston

177

18

Seattle

162

18

Miami

192

19

St. Louis

145

19

Washington D.C.

207

20

Washington D.C.

207

20

New York

245

Total

3181
Median =

Total (Room Rates for 20

Hotels)

3181

No. of Cities
Mean

20
159.05

Median =

Value of (n+1)/2 th observation

=(20+1)/2
=10.5
161

Mode

167

Solution (D) : First Quartile

Q1 =(1 x n x 1) / 4 th Observation
=(1*20*1)/4
=5th Observation
Q1 =134

Solution (E) : Third Quartile

Q3 =(3 x n x 1) / 4 th Observation
=(3*20*1)/4
=15
Q3 =167

Sr.#.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

3 points shots
23
20
17
18
13
16
8
19
28
21
17
19
22
25
15
10
11
25
23
350

shots made
4
6
5
8
4
4
5
8
5
7
7
10
7
11
6
5
3
8
7
120

a.
b.

No. of 3 point shots taken per game =

No. of 3 point shots made per game =

18
6

Solution (A) : Mean

Sr.#.
1
2
3
4
5
6
7
8
9
10

University
Columbia
Harvard
M.I.T
Michigan
Northwestern
Princeton
Stanford
Texas
Texas A & M
Yale
Total
Total Endowment
No .of Universities
Mean

Solution (B) : Median

Endowment $Billions

Sr.#.

7.2
36.6
10.1
7.6
7.2
16.4
17.2
16.1
6.7
22.9
148

1
2
3
4
5
6
7
8
9
10

148
10
14.8

University
Texas A & M
Columbia
Northwestern
Michigan
M.I.T
Texas
Princeton
Stanford
Yale
Harvard

Solution (C) : Mode

Endowment
$Billions

Mode

7.2

6.7
7.2 Solution (D) : First Quartile
7.2
7.6
Q1 =(1 x n + 1) / 4 th Observation
10.1
=2.5 th observation
16.1
Q1 =7.2
16.4
17.2
22.9 Solution (E) : Third Quartile
36.6
Q3 =(3n + 1) / 4 th Observation
=(3*10+1)/4
=7.75
Median = Value of (n+1)/2 th observation
Q3
=17
=(10+1)/2
=5.5
Median =

13.1

e. The toal endowment of all these 10 universities is $148 billions. As per statement

Solution (A) : Mean

cost of customer
purchases

Sr.#.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Total

120
130
105
100
230
150
360
115
110
105
120
180
115
195
120
235
160
155
140
255
3200

Mean =

160

Median =

Solution (A) : Median

cost of
Sr.#.
customer
purchases
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

100
105
105
110
115
115
120
120
120
130
140
150
155
160
180
195
230
235
255
360

Value of (n+1)/2 th
observation

=(20+1)/2
=
Median =

10.5
135

Mode = 120

Solution (D) : First Quartile

I =20 / 4 th observation
=5th observation
Q1 =115
Solution (D) : Third Quartile
I =(75/100) 20 th observation
=(3*20+1)/4
=15.25
Q3 =183.75

Solution (D) : 90th Percentile

I =(90 / 100) 20 th Observation
=(90x20+1) / 100 th observation
=18.01
P90 =245

Sr.#.
Existing Homes
1
315.5
2
202.5
3
140.2
4
181.3
5
470.2
6
169.9
7
112.8
8
230
9
177.5
Total
1999.9
Mean

222.21

Ordered Values
Sr.#.
Existing Homes
1
112.8
2
140.2
3
169.9
4
177.5
5
181.3
6
202.5
7
230
8
315.5
9
470.2

New Homes
275.9
350.2
195.8
525
225.3
215.5
175
149.5
2112.2
264.03

New Homes
149.5
175
195.8
215.5
225.3
275.9
350.2
525

Median =
=
=
Difference =

(9+1)/2
5th observation
181.3
39.1

(8+1)/2
4.5
220.4

The calculations shows that the raise in median sales prices of new homes is higher than
the existing homes sales and difference is $39.1 thousands.
c. New Homes sales price are higher than existing home prices
The difference between existing and new home prices is 39.1
d. One year earlier the median sales prices of existing homes was $208.4
One year earlier the median sales prices of new homes was $249.

Existing Homes

One year ealirer price ($) =

9 years median price ($) =
Difference ($) =
Difference in %age =

208.4
181.3
27.1
13.0%

New Homes

One year ealirer price ($) =

9 years median price ($) =
Difference ($) =
Difference in %age =

249
220.4
28.6
11.5%

e. First the difference in sales prices for existing and new homes from one year
earlier prices, the %age impact in existing homes is higher than the new homes

Sr.#.

GDP forecasts

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

2.6
2.7
0.4
3.1
2.7
2.5
2.3
2.7
2.2
2.7
2.9
1.9
3.4
3.1
1.8
0.9
2.8
1.1
2.6
1.7
2
2.8
2.3
2.1
2
2.8
2.5
2.4
3.5
0.5

ordered
GDP
forecasts
0.4
0.5
0.9
1.1
1.7
1.8
1.9
2
2
2.1
2.2
2.3
2.3
2.4
2.5
2.5
2.6
2.6
2.7
2.7
2.7
2.7
2.8
2.8
2.8
2.9
3.1
3.1
3.4
3.5

Solution (a)
Minimum Forecast
Minimum Forecast

0.4
3.4

Solution (b)
Mean (%) =

2.3
(30+1)/2 th
Median (%) =observation
=
15.5
=
2.5
Mode (%) =
2.7

Solution (c)
Q1 (%) =(30+1)/4 th observation
=
7.75
First Quartile (%) =
2.0
Q3 (%) =(3(30)+1)/4 th observation
=
22.75
Third Quartile (%) =
2.8
Solution (d)
Arithmatic shows that the forecasts of economists is optimistic

Ordered data

Mean =

City

Highway

13.2

17.2

14.4

17.4

15.2

18.3

15.3

18.5

15.3

18.6

15.3

18.6

15.9

18.7

16

19

16.1

19.2

16.2

19.4

16.2

19.4

16.7

20.6

16.8

21.1

City

Highway

15.58

18.92

Median =(13+1)/2 th observation

=7 th Observation
=

15.9

18.7

Mode =

15.3

18.6, 19.4

Sr.#.
1
2
3
4
5
6
7
8
9
10
11
12
13

City
16.2
16.7
15.9
14.4
13.2
15.3
16.8
16
16.1
15.3
15.2
15.3
16.2

Highway
19.4
20.6
18.3
18.6
19.2
17.4
17.2
18.6
19
21.1
19.4
18.5
18.7

Conclusion :
All three performance measures are showing that the mileage at
Highway is better than City.

Disney Movies
Sr.#.
1
2
3
4
5
6
7
8
9
10
11
12
13

Revenue ($millions)
104
110
136
169
249
250
253
273
304
325
346
354
448

Total Revenue =

3321

Mean =

255.5

Pixar Movies
Sr.#.
1
2
3
4
5
6

Total Revenue =

3231

Mean =

538.5

Median =(6+1)/2 th observation

=3.5th observation
=
505.0
Mode =

Median =(13+1)/2 th observation

=7th Observation
=
169.0
Mode =

Revenue ($millions)
362
363
485
525
631
865

363.0

Q1=(6+1)/4 th observation
=1.75th observation
=
362.8

169.0

Conclusion :
Q1=(13+1)/4 th observation
=3.5th observation
=
152.5

Maxima on the part of revenue of Pixar and Disney movies shows in the following
statistics that Pixar's revenue is greater than Disney movies.

Sr.#.
1
2
3
4
5
6
Total

Bowler's score
168
170
174
182
184
190
1068

X-U
-10.0
-8.0
-4.0
4.0
6.0
12.0
0

Range =Maximum - Minumum Value

=
22.0
Mean =

178.0

Variance =

75.2

Std. Dev. =

8.7

C.V (%) =

4.9

(X-U)2
100.0
64.0
16.0
16.0
36.0
144.0
376.0

Sr.#.

Models with
DVD Players ($)

Models without
DVD Players ($)

1
2
3

300
400
400

290
300
300

4
5
Total

450
500
2050

300
360
1550

Solution (A)
Mean ($)=
Min. Value =
Max. Value =
Range =

410.0
300
500
200.0

310.0
290
360
70.0

To buy the model with DVD player, on average

$100 will be paid.

Models with DVD Players in Dollars

Models with
DVD
Sr.#.
Players ($)
1
450
2
300
3
400
4
500
5
400
Total

(X-Xbar)

(X-Xbar)2

40.0
-110.0
-10.0
90.0
-10.0
0.0

1600.0
12100.0
100.0
8100.0
100.0
22000

Variance =
Std. Dev. =
Models without DVD Players in Dollars
Models without
Sr.#.
DVD Players ($)
1
300
2
300
3
360
4
290
5
300
Total

5500.0
74.2

(X-Xbar)

(X-Xbar)2

-10.0
-10.0
50.0
-20.0
-10.0
0.0

100.0
100.0
2500.0
400.0
100.0
3200

Variance =
Std. Dev. =

800.0
28.3

Conclusion :
Standard variation of models with and without DVD players shows that when anybody like to buy models from
market he found that he has to pay a greater amount in case of DVD player rather than without DVD player.

Sr.#.

Car Rental Rates

Sr.#.

Car Rental Rates

(X-Xbar)

(X-Xbar)2

1
2
3
4
5
6
7
Total

43
35
34
58
30
30
36
266

1
2
3
4
5
6
7

43
35
34
58
30
30
36

5.0
-3.0
-4.0
20.0
-8.0
-8.0
-2.0
0.0

25.0
9.0
16.0
400.0
64.0
64.0
4.0
582

Mean ($)=
Min. Value =
Max. Value =
Range =

Total

Variance =
Std. Dev. =

38.0
30
58
28.0

Western Cities
Western citiies mean car rent =
Variance =
St. Dev. =

97.0
9.85

Eastern Cities
$38
12.3
3.5

Western citiies mean car rent =

Variance =
St. Dev. =

$38
97
9.8

Conclusion :
Statistics shows that eastern cities having more variation like 97 against 12.3 and similarly standard
deviation $9.8 against $3.5 of western cities.

Pomona Data
Sr.#.
1
2
3
4

Air Quality Index

28
42
58
48

5
6
7
8
9
Total
Mean ($)=
Min. Value =
Max. Value =
Range =

45
55
60
49
50
435
48.3
28
60
32.0

Pomona Data
Sr.#.
Air Quality Index
1
28
2
42
3
58
4
48
5
6
7
8
9

45
55
60
49
50
Total :

(X-Xbar)
-20.3
-6.3
9.7
-0.3

(X-Xbar)2
413.4
40.1
93.4
0.1

-3.3
6.7
11.7
0.7
1.7
0.0

11.1
44.4
136.1
0.4
2.8
742.0

Variance =
Std. Dev. =

Anaheim Data
Mean
Variance
Std. Deviation

X bar =
s2=
s=

48.5
136
11.66

92.8
9.63

Conclusion(c) :

statistics shows that Air Index Quality of Pomona is better than Anaheim due to the lower standard deviation of
9.63 against 11.66.

Dawson Supply

Clark Distributions
Days of
Sr.#.
Delivery

Sr.#.

Days of
Delivery

(X-Xbar)

(X-Xbar)2

1
2
3
4
5
6
7
8
9
10
Total

11
10
9
10
11
11
10
11
10
10
103

0.7
-0.3
-1.3
-0.3
0.7
0.7
-0.3
0.7
-0.3
-0.3
0.0

0.5
0.1
1.7
0.1
0.5
0.5
0.1
0.5
0.1
0.1
4.1

1
2
3
4
5
6
7
8
9
10
Total

8
10
13
7
10
11
10
7
15
12
103

0.5
0.67

Mean (days)=
Min. Value =
Max. Value =
Range =

10.3
7
15
8.0

Mean (days)=
Min. Value =
Max. Value =
Range =

10.3
9
11
2.0

Variance =
Std. Dev. =

(X-Xbar)

(X-Xbar)2

-2.3
-0.3
2.7
-3.3
-0.3
0.7
-0.3
-3.3
4.7
1.7
0.0

5.3
0.1
7.3
10.9
0.1
0.5
0.1
10.9
22.1
2.9
60.1

Variance =
Std. Dev.=

6.7
2.58

Conclusion(c) :
Statistics shows that Dawson Supply distribution is more reliable due to Clark distribution because they ae deviating lesser than
clark dist. With .67 days rather than 2.58 std. dev. Of Clark distribution, also if we see on mean both distributions services are
supplying equally.

City Areas
Sr.#.
1
2
3
4
5
6
Total
Mean (days)=
Min. Value =
Max. Value =
Range =

Cost ($)
33
27
32
38
36
32
198
33.0
27
38
11.0

(X-Xbar)
0.0
-6.0
-1.0
5.0
3.0
-1.0
0.0
Variance =
Std. Dev. =
C.V.=

(X-Xbar)2
0.0
36.0
1.0
25.0
9.0
1.0
72.0
14.4
3.79
11.50%

Retirement Areas
Sr.#.
Cost ($)
1
29
2
32
3
32
4
34
5
34
6
31
Total
192
Mean (days)=
Min. Value =
Max. Value =
Range =

32.0
29
34
5.0

(X-Xbar)
-3.0
0.0
0.0
2.0
2.0
-1.0
0.0
Variance =
Std. Dev.=
C.V.=

(X-Xbar)2
9.0
0.0
0.0
4.0
4.0
1.0
18.0
3.6
1.90
5.93%

Conclusion:
Statistics shows that standard deviation of Retirement areas is 1.90 against 3.79 of City areas and the mean value of both are
showing that Retirement Areas costs on average are 32 against City areas 33. Both facts proves that Grocery costs of Retirement
areas are better than City areas and there is an appeal for customers to save money. Similarly C.of Variation are showing that
Retirement areas having lesser variance than City Areas.

Web File -------- Data not provided

2005 season
Sr.#.
1
2
3
4
5
6
7
8
Total
Mean (days)=
Min. Value =
Max. Value =
Range =

scores

(X-Xbar)

(X-Xbar)2

2006 season
Sr.#.

74
78
79
77
75
73
75
77
608

-2.0
2.0
3.0
1.0
-1.0
-3.0
-1.0
1.0
0.0

4.0
4.0
9.0
1.0
1.0
9.0
1.0
1.0
30.0

1
2
3
4
5
6
7
8
Total

71
70
75
77
85
80
71
79
608

76.0
73
79
6.0

Variance =
Std. Dev. =

4.3
2.07

Mean (days)=
Min. Value =
Max. Value =
Range =

76.0
70
85
15.0

C.V.=

2.72%

scores

(X-Xbar)

(X-Xbar)2

-5.0
-6.0
-1.0
1.0
9.0
4.0
-5.0
3.0
0.0

25.0
36.0
1.0
1.0
81.0
16.0
25.0
9.0
194.0

Variance =
Std. Dev.=
C.V.=

27.7
5.26
6.93%

Conclusion:
Statistics are showing that both years having seam mean value, but when we look at the variance and standard deviations the
scores of 2005 are better than 2006 seanson and this also results that Co efficienct of varation of 2005 is 2.7 rather than 6.93 of
2006 season. and no improvement is seeing in 2006 season.

Quarter Mile Times

Sr.#.
1
2
3
4
5
Total

time
0.92
0.98
1.04
0.9
0.99
4.83

Mean (days)=
Min. Value =
Max. Value =
Range =

1.0
0.9
1.04
0.1

(X-Xbar)
-0.046
0.014
0.074
-0.066
0.024
0.0
Variance =
Std. Dev. =
C.V.=

(X-Xbar)2
0.002
0.000
0.005
0.004
0.001
0.013
0.003
0.0564
5.84

Mile Times
Sr.#.
1
2
3
4
5
Total

time
4.52
4.35
4.6
4.7
4.5
22.67

(X-Xbar)
-0.014
-0.184
0.066
0.166
-0.034
0.0

Mean (days)=
Min. Value =
Max. Value =
Range =

4.5
4.35
4.7
0.4

Variance =
Std. Dev. =
C.V.=

(X-Xbar)2
0.000
0.034
0.004
0.028
0.001
0.067
0.017
0.1295
2.86

Conclusion:

Results shows that quarter miles are most consistent due to lower standard deviation .0564 as compare to Mile times which are
.1295. This also showed in C.V%age that is 5.84% of Quarter Miles as compare to 2.86% of Mile Times. Coach is saying true.