Midterm Revision (STAT215)

1. The probability of a student getting an A in an economics class is .24 and

that of getting a B is .28. What is the probability that a randomly selected
student from this class will get an A or a B in this class?

2. For an experiment P(A) =.42, P(B)=.29, and P (A or B) =.71.

Find P (A and B) and P(A/B). Are A and B mutually exclusive events? Are
they independent events?

3. The following data represents the time in seconds clients spent in the
National bank finishing their transactions, complete the following table.

18 18 18 19 19 19 19 19 19 19 19 20 20 20 21 21 21 21
21 21 22 22 22 22 22 23 23 23 23 23 23 24 24 25 25 25
25 25 25 26 26 27 27 28 29 30 30 31 35 35

Time 18-21 21-24 24-27 27-30 30-33 33-36

Interval
Frequency
Cumulative
Frequency

4. The following data give the number of new cars sold at a dealership during
a 20-day period.

8 5 12 3 9 10 6 3 8 8 4 6 10 11 7 7 3 5 9 11

a) Calculate the values of the three quartiles.

b) Find the (approximate) value of the 35th percentile. Give a brief
interpretation of this percentile.
c) Find the percentile rank of 7. Give a brief interpretation of the percentile
rank.
d) Calculate the mean, median and mode.
e) Calculate the range, variance, standard deviation and coefficient of
variation.
f) Calculate coefficient of skewness.
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5. The following histogram represents the computer output of waiting times
of a sample of 50 persons waiting at bus station in Cairo in minutes.

Histogram of age
18

16

14

12
Frequency

10

0
18 21 24 27 30 33 36
age

Use the information in the above Histogram to complete the following Table

Classes Frequencies Relative Cumulative

Frequencies frequency
18-21
21-24
24-27
27-30
30-33
33-36
Total

Use the information you have completed in the table to answer the following
questions
1. What is the relative frequency of the third class?
2. What percentage of individuals wait more than 27 minutes to ride the bus?
3. What percentage of customers wait between 21 and 30 minutes to ride the
bus?
4. What is the class width?
5. If we present the first and the last columns graphically, what is the name
of the displayed graph?
6. What is the shape of the frequency distribution of waiting time?
(a) Skewed to left (b) Skewed to right (c) Symmetric

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 6. All the 420 employees of the company were asked whether or not they
smoke and whether or not they are college graduates. Based on this
information, the following two-way classification table was prepared.

College Graduate Not a College Graduate

Smoker 35 80
Nonsmoker 130 175

Suppose one employee is selected at random from this company, find the
following probabilities.
a. P (college graduate or smoker)
b. P (smoker or not a college graduate)
c. P (smoker or nonsmoker)

7. The following table gives a two-way classification of 200 randomly

selected purchases made at a department store.

Paid by cash/check Paid by credit card

Male 24 46
Female 77 53

a. If one of these 200 purchases is selected at random, find the probability that
it is:
i.
ii. made by a female
iii. paid by cash/check
iv. paid by credit card given that the purchase is made by a male.
v. made by a female given that it is paid by cash/check.
vi. made by a female and paid by a credit card.
vii. Paid by cash/check or made by a male.

b. Are the events “Female” and “paid by credit card” independent? Are they
mutually exclusive? Explain why or why not.

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8. Assume that the following data represent the number of expatriate students
in 40 schools in 6th of October city

18 8 44 72 25 28 4 37 23 80
61 97 61 60 90 29 15 50 83 36
102 22 3 63 52 42 55 34 79 47
46 51 33 85 116 37 29 43 33 26

a) Construct a frequency distribution to organize these data. Use the

following classes 0-20, 20-40, 40-60, 60-80, 80-100 and 100-120.
b) Present the above data in a graph and specify the nature of the data.
What does it indicate?
c) What is the percentage of schools that have 60 or more expatriate
students in their classes?

9. Petrol consumption of 75 cars has been measured in miles per gallon

(MPG) to study it. The measurements are displayed in a frequency table
shown below

Petrol Absolute
consumption (MPG) frequencies
12 to 15 8
15 to 18 10
18 to 21 20
21 to 24 13
24 to 27 12
27 to 30 4
30 to 33 3
33 to 36 3
36 to 39 0
39 to 42 2

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a) Present the above data in a graph and specify the nature of the data. What
does it indicate?
b) What percentage of cars has a consumption rate more than or equal to 27
MPG?

10. Assume that 160 students are registered for the Microeconomics course
this semester at the Faculty of Management Sciences of MSA University.
Students come from the four majors offered: Marketing and International
Business, Accounting, Management Information Systems (MIS) and
Economics. The following table shows the distribution of students with
respect to gender and major.

Marketing Accounting MIS Economics Total

Male 30 40 10 17 97
Female 28 18 5 12 63
58 58 15 29 160

a) What percentage of these students came from the Economics department?

b) What is the percentage of these students who are males and from
Management (Marketing) department?
c) What percentage of these students are from MIS or Management
(Marketing) departments?
d) If one student is selected at random, find the probability that she will be a
female given that she is from the accounting department

11. The following table was produced using the SPSS package.

a) What is the range for English Exam?

b) What is the variance for Math Exam?
c) What is the coefficient of variation for Reading?
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Choose the correct answer:

1. The sample size

A. ? can be larger than the population size

B. ? is always smaller than the population size

C. ? can be larger or smaller than the population

D. ? is always equal to the size of the population

2. A population is

A. ? the same as a sample

B. ? the selection of a random sample

C. ? the collection of all items of interest in a particular study

D. ? none of the above

3. The study of the methods of organization, summarization, and

presentation of statistical data is referred to as

A. ? inferential statistics

B. ? descriptive statistics

C. ? sampling
D. ? none of the above

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4. The process of making inferences about the characteristics of the
population based on the sample information is termed

A. ? descriptive statistics

B. ? random sample
C. ? statistical inference
D. ? sampling

5. The entities on which data are collected are

A. ? variables
B. ? data sets

C. ? elements

D. ? none of the above

6. The level of measurement that allows for the rank ordering of data
items is

A. ? nominal measurement
B. ? ratio measurement

C. ? ordinal measurement

D. ? none of the choices are correct

7. A characteristic of interest for the elements is

A. ? a variable

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 B. ? an element

C. ? a data set
D. ? none of the above

8. Arithmetic operations are appropriate for

A. ? qualitative data

B. ? quantitative data

C. ? both quantitative and qualitative data

D. ? neither quantitative nor qualitative data

E. ? none of the above

10. From a sample of students in your statistics class, you collect the
following: the student's name, gender, STAT score, age, and their grade
in a freshman level math class. The variable student's name is measured
on which scale of measurement?

A. ? Nominal
B. ? Ordinal

C. ? Interval

D. ? Ratio

11. The variable student's gender is measured on which scale of

measurement?

A.? Nominal
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 B? Ordinal

C? Interval

D? Ratio

12. The variable student's STAT score is measured on which scale of

measurement?

A? Nominal

B? Ordinal

C? Interval

D? Ratio

13. The variable student's age is measured on which scale of

measurement?

A? Nominal

B? Ordinal

C? Interval

D? Ratio

14. The variable student's grade in a freshman level math class (A, B,
C, D, or F) is measured on which scale of measurement?

A? Nominal

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 B? Ordinal

C? Interval

D? Ratio

15. The variable student's name is an example of a quantitative

variable.

A? True

B? False

16. The variable student's age is an example of a quantitative variable.

A? True

B? False

17. The variable student's gender is an example of a quantitative

variable.

A? True

B? False

18. A tabular summary of a set of data, which shows the frequency of

the appearance of data elements in several non-overlapping classes is
termed

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 A? the class width

B? a frequency polygon

C? a frequency distribution

D? a histogram

E? none of the above

19. A tabular summary of a set of data showing classes of the data and
the fraction of the items belonging to each class is called

A? the class width

B? a relative frequency distribution

C? a cumulative relative frequency distribution

D? an ogive

E? none of the above

20. A histogram

A? A graphical presentation of a frequency or relative frequency

distribution

B? a graphical method of presenting a cumulative frequency or a

cumulative relative frequency distribution

C? The history of data elements

D? none of the above

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 21. A graphical method of presenting qualitative data by frequency
distribution is termed

A? a frequency polygon
B? an ogive
C? a bar graph
D? none of the above

22. The sum of frequencies for all classes will always equal

A? 1
B? the number of elements in a data set
C? the number of classes
D? a value between 0 to 1
E? none of the above

23 The relative frequency of a class is computed by

A? dividing the midpoint of the class by the sample size
B? dividing the frequency of the class by the midpoint
C? dividing the sample size by the frequency of the class
D? dividing the frequency of the class by the sample size
E? none of the above

24.The length of the interval forming a class is called

A? the class midpoint

B? the lower-class limit

C? the upper-class limit

D? the class width

E? none of the above

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25. You are given the following frequency of grades for a Business
Statistics class
Grade Frequency
A 10
B 15
C 15
D7
F3
50
What is the relative frequency of the D grade?
A? 0.07
B? 0.14
C? 7
D? 14
E? 50.4
26. What is the relative frequency of the B grade?

A? 0.15
B? 0.30
C? 30
D? 108
E? None of the above

27. When constructing a pie chart, how many degrees would be in the
section of the pie showing the F grade?
A? 0.06
B? 6
C? 21.6
D? None of the above
28. A bar graph is appropriate when summarizing
A? quantitative data
B? qualitative data

29. A histogram is appropriate when summarizing

A? quantitative data
B? qualitative data

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 30. Define ogive
A? A percent frequency distribution
B? A graph of a cumulative distribution
C? A tabular summary of data for two variables
D? The beginning of the song "Home on the Range."

31. The last entry in a cumulative relative frequency distribution is

always one.
A? True
B? False

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