MATH
251-B Midterm
November 2, 2005
Questions
1.
The following data
set provides a snapshot of the financial performance of Ameritech Corporation
(Barron’s, December 29, 1997)
|
|
1993
($) |
1994
($) |
1995
($) |
1996
($) |
|
Earning Per Share Revenues (billion) Net Income (billions) Book Value Per Share |
2,78 11,87 1,51 14,35 |
2,13 12,57 1,17 10,98 |
3,41 13,43 1,89 12,67 |
3,83 14,92 1,12 13,98 |
a.
How Many Variables Are There?
b.
Are the data qualitative or
quantitative
c.
Are they cross-sectional or time
series data? Why?
2.
The US Bureau of the
Census publishes a variety of information on the
Following
is the percent frequency distribution of the
|
Age |
Percent
Frequency |
|
0-13 14-17 18-24 25-34 35-44 45-54 55-64 65 or over |
20,0 5,7 9,6 13,6 16,3 13,5 8,7 12,6 |
|
Total |
100,0 |
a.
What percentage of
the population is 34 years old or less?
b.
What percentage of
the population is over 34 years old?
c.
What percentage of
the population is between 25 and 54 years inclusively?
d.
The total population
is 275 million. How many people are less than 25 years old?
3.
|
|
Occupation |
Satisfaction Score |
|||
|
1 |
Lawyer |
42 |
11 |
Lawyer |
53 |
|
2 |
Physical Therapist |
86 |
12 |
Cabinetmaker |
65 |
|
3 |
Lawyer |
42 |
13 |
Lawyer |
74 |
|
4 |
Systems Analyst |
55 |
14 |
Physical Therapist |
52 |
|
5 |
Lawyer |
38 |
15 |
Physical Therapist |
78 |
|
6 |
Cabinetmaker |
79 |
16 |
Systems Analyst |
44 |
|
7 |
Lawyer |
44 |
17 |
Systems Analyst |
71 |
|
8 |
Systems Analyst |
41 |
18 |
Lawyer |
50 |
|
9 |
Physical Therapist |
55 |
19 |
Lawyer |
48 |
|
10 |
Systems Analyst |
66 |
20 |
Cabinetmaker |
69 |
a.
Provide a
cross-tabulation of occupation and job satisfaction score.
b.
Compute the row
percentage for your cross-tabulation in part (a)
c.
Compute the Frequency
distribution for occupation
d.
Compute the Relative
Cumulative Frequency distribution for occupation
4.
Suppose IQ scores
have a bell-shaped distribution with a mean of 90 and St. Dev. of 10.
a.
What percentage of people
has an IQ score between 80 and 100?
b.
What percentage of
people has an IQ score between 70 and 110?
c.
What percentage of
people has an IQ score more than 120?
5.
4,00 4,12 3,82 4,00 4,56 2,14 2,32 3,11 4,88 3,05
a.
Provide a five-number
summary
b.
Compute the lower and
upper limits
c.
Is there any
outliers?
d.
Show the box plot of
above variables
6.
Five observations
taken for two variables below.
|
x |
4
6 11 3
16 |
|
y |
50 50 40
60 30 |
a.
Develop a scatter
diagram and interpret it
b.
Compute and interpret
covariance
c.
Compute the sample
correlation coefficient for the data.
d.
What does this value
tell us about the relationship between two variables?
Not:
You can use your simple calculators. Cell phones are not allowed in this exam.
You can use 1 sheet summaries of your class notes. Each
question is 20 point. GOOD LUCK
Mehmet
Emin Şan
Solutions
1.
a) 16 variables
b) Quantitative
data because data indicates how much or how many of something.
c) Cross-Sectional because data collected at
same or approximately the same point in time.
2.
a) 20%+5,7%+9,6%+13,6%=48,9% of
population is less then or equal to 34 years old
b) 16,3 %+13,5%+8,7%+12,6%=51,1%
population is over 34 years old
c) 13,6 %+16,3%+13,5%=43,4% population
is between 25 and 54 years old
d)
20%+5,7%+9, %6=35,6% population is less
than 25 years old so 275 million*0,356=97,075 million people less then 25 years
old.
3.
a) I picked 5 as my class number so
Class Width=(86-38)/5 = 9,6 so My Class Width is 10
|
Score |
L |
PT |
SA |
CM |
Total |
|
30-39 40-49 50-59 60-69 70-79 80-89 |
1 4 2 0 1 0 |
0 0 2 0 1 1 |
0 2 1 1 1 0 |
0 0 0 2 1 0 |
1 6 5 3 4 1 |
|
Total |
8 |
4 |
5 |
3 |
20 |
b)
|
Score |
L |
PT |
SA |
CM |
Total |
|
30-39 40-49 50-59 60-69 70-79 80-89 |
1/1*100=100 4/6*100=66,66 2/5*100=40 0 1/4*100=25 0 |
0 0 2/5*100=40 0 1/4*100=25 1/1*100=100 |
0 2/6*100=33,33 1/5*100=20 1/3*100=33,33 1/4*100=25 0 |
0 0 0 2/3*100=66,66 1/4*100=25 0 |
1/1*100=100 6/6*100=100 5/5*100=100 3/3*100=100 4/4*100=100 1/1*100=100 |
c)
and d)
|
Occupation |
F |
RF |
CRF |
|
L PT SA CM |
8 4 5 3 |
0,4 0,2 0,25 0,15 |
0,4 0,6 0,85 1,00 |
4.
a)
Z-score for 100 is (100-90)/10 =1 since the shape of the data is given as
bell-shaped then by empirical rule 68% got the IQ scores between 90 and 100
b)
Z score we can calculate like above and we get 2 by empirical rule 95% got the
score between 70 and 110
c)
Z-score for 120 is 3 so by empirical rule almost all members are between 60 and
120 there fore almost no elements more than 120 and less then 60.
5.
a)
five-number summary
Q1=3,05 Q2= 3,91 Q3=4,12 Smallest # 2,14 Largest# 4,88
b)
LL= Q1-1,5*(IQR) IQR=Q3-Q1=4,12-3,05=1,07 so LL=1,45
UL=Q3+1,5*(IQR) UL=5,72
d)
BOX PLOT
c)
According to Box Plot above there are no outliers.
6.
a)
As
we can see from the picture above there is a negative relation
between x and y
b)
Covariance is -48 (but you must calculate the number. Providing only number is
no credit)
c)
rxy= -0,77
again providing only the number is not
acceptable.
d)
so there is a strong – relation
between two variables
Midterm
Statistics
|
Math251-B 1. Midterm |
|
|
Only
Attanded Student |
|
|
Mean |
42,69230769 |
|
Median |
42,5 |
|
Mode |
40 |
|
Standard
Deviation |
25,25512895 |
|
Sample
Variance |
637,8215385 |
|
Range |
97 |
|
Minimum |
0 |
|
Maximum |
97 |
|
Count |
26 |
|
First
Quartile |
23 |
|
Second
Quartile |
60 |
|
Math251-B 1. Midterm |
|
|
With
Everyone |
|
|
Mean |
28,46153846 |
|
Median |
21 |
|
Mode |
0 |
|
Standard
Deviation |
28,90169013 |
|
Sample
Variance |
835,3076923 |
|
Range |
97 |
|
Minimum |
0 |
|
Maximum |
97 |
|
Count |
39 |
|
First
Quartile |
0 |
|
Second
Quartile |
52 |
