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Business Statistics I (QMS102) - Test 1 REVIEW PROBLEMS
Question 1 Consider the following questions being asked on a survey. What is the measurement scale of the response data? (a) Ordinal (b)Nominal (c) Interval (d)Ratio – Discrete (e) Ratio - Continuous 1) What was the rating of the hotel that you last stayed in? a) Dissatisfied b) Somewhat Dissatisfied c) Somewhat satisfied d) Satisfied e) Very good 2) What is your marital status? 1=Married; 2=Common Law; 3=Widowed; 4=Divorced; 5=Single 3) What is the major that you are studying? a) Math b) Physics c) Chemistry d) Biology e) History 4) What is the postal code? 5) Which letter grade did you get on your Chemistry course last term? 6) What is the color of your eyes? 7) What is the color of your car? 8) Where is your hometown? 9) How many courses are taking this term? 10) How much time do you spend on shopping each week? 11) What was the lowest temperature in 0 C in the city you are living last month? 12) How many children do you intend to have? 13) How many languages can you speak? 14) Which language is your native language? 15) Where were you born? 16) What is your weight? 17) How long does it take for you to walk from your home to Ryerson?
NOTE: Questions 2 – 3 are based on the following information.
The following data represents the heights (m) for a sample of 11 boys at age 12. 1.38, 1.43, 1.25, 1.47, 1.29, 1.54, 1.37, 1.25, 1.53, 1.45, 1.29 Question 2 If you were to construct a stem-and-leaf display using the rules discussed in lectures for the above data, how many stems should your stem-and-leaf display have? a) 7 b) 8 c) 6 d) 9 e) None of these Question 3 Based on the stem-and-leaf display (using the rules discussed in lectures) for the above data, how many leaves would there be on the second stem of your stem-and-leaf display? a) 4 b) 0 c) 2 d) 3 e) None of these NOTE: Questions 4 - 7 are based on the following information. The following data represents the heights (m) for a sample of 12 boys at age 12. 1.38, 1.43, 1.25, 1.47, 1.29, 1.54, 1.37, 1.25, 1.53, 1.45, 1.29, 1.41 Question 4 If you were to construct a frequency distribution using the rules discussed in lectures for the above data, what would the class width (in thousand dollars) be? a) 1.0 b) 0.05 c) 0.50 d) 0.10 e) 0.025 Question 5 If you were to construct a frequency distribution using the rules discussed in lectures for the above data, how many classes are there in the frequency distribution? a) 4 b) 5 c) 8 d) 6 e) 10 Question 6 Based on the frequency distribution using the rules discussed in lectures for the above data, what is the relative frequency of the fourth class? (The answers provided below are rounded to three decimal places). a) 0.250 b) 0.333 c) 0.375 d) 0.167 e) None of these Question 7 Based on the frequency distribution using the rules discussed in lectures for the above data, what is the cumulative percentage of up to and including the third class? (The answers provided below are rounded to two decimal places). a) 16.67% b) 33.33% c) 50.00% d) 46.67% e) None of these
Use the following data for questions 8 to 10 inclusive.
The following table represents the distribution of the income ($1000) in 2011 for a sample of households in Toronto. Table 1 Income ($1000) Number of households 20 and under 37 30 30 and under 22 40 40 and under 45 50 50 and under 5 60 60 and under 20 70 70 and under 11 80 80 and under 15 90 Question 8 The number households in this sample, whose incomes in 2011 are lower than $70,000, is a) 12.9% b) 16.8% c) 73.5% d) 83.2% e) 80.3%
Question 9 The relative frequency of the households in this sample, whose incomes in 2011 are higher than $50,000, is (rounded to three decimal places): a) 0.671 b) 0.032 c) 0.329 d) Cannot be determined from the table e) None of the above Question 10 The class width (in $1000) for the classes in this table is: a) 10,000 b) 5,000 c) 10 d) 5
e) 25
Note: Questions 11-13 are based on the following information Forty-five students wrote the PCS105 midterm test last week. The following stem-and-leaf display shows the grades of students who failed PCS105 midterm test last week. Stem
Leaf
( ×10 ) 0 1 1 2 2 3 3 4
78 012 59 00 556 89 13
Question 11 What is the maximum value in the above data? a) 40.3 b) 4.3 c) 4.03 d) 43
e) 41.3
Question 12 How many students passed the last week’s PCS105 midterm test? a) 15 b) 16 c) 23 d) 29 e) 25 Question 13 What is the failure rate of this test? a) 64.44% b) 35.56% c) 25.72%
d) 24.73%
e) 14.32%
Note: Questions 14 – 17 are based on the following Ogive.
The length of stay, t days, that each of 500 guests stayed at a five star hotel was recorded and the results used to construct the Ogive below. Note that the first class is “0 and under 5” and the last class is “35 and under 40”.
Question 14 How many guests have stayed in this hotel at least 20 days? a) 300 b) 200 c) 150 d) 350
e) 100
Question 15 How many guests (in percentage) stayed in this hotel 15 days or less? a) 40% b) 60% c) 70% d) 35% e) cannot be determined Question 16 Find the approximate average length of stay per guest. a) 18 b) 19 c) 19.5 d) 18.5
e) cannot be answered
Question 17 Find the 70th percentile: a) 35 b) 25
e) cannot be answered
c) 15
d) 22.5
Question 18 is based the following information. The answer is rounded to one decimal place. Forty-five students wrote the PCS105 midterm test last week. The following stem-and-leaf display shows the grades of students who failed PCS105 midterm test last week. Stem ( ×10 ) 0
Leaf 78
1 1 2 2 3 3 4
012 59 00 556 89 13
Question 18 The 75th percentile of the above data is: a. 26 b. 38 c. 32 d. 25.5
e. 36.5
Use the following data for Question 19. Question 19 The following table shows some data regarding the top 5 grocery chains in Toronto. Table 1 Chains A B C D E
Number of Stores 33 21 25 12 25
Annual Revenue per store($000) 69800 42980 38900 28905 54300
Total Profit ($Million) 22 15 19 12 26
a) What is the overall mean annual revenue per store for the five chains shown? b) What is the overall mean profit per store? c) What is the overall mean profit per chain for the five chains shown? Question 20
Question 21 Construct a bar chart that represents the data in Question 20.
Question 22 Twnty-nine executives reported the number of telephone calls made during a randomly selected week as shown here. Construct a stem-and-leaf plot. 24 5 7
15 22 16
12 8 56 12 18 36 29 35 24 8 26 29 53
12 33
15 58
43 32
10 15 46 19
Question 23 Twnty-nine executives reported the number of telephone calls made during a randomly selected week as shown here. 24 15 12 8 56 12 18 12 15 43 10 15 5 22 36 29 35 24 8 33 58 32 46 19 7 16 26 29 53 Construct a frequency distribution.
Question 24 Construct a relative frequency distribution from the data in Question 23. Question 25 Construct a cumulative frequency distribution from the data in Question 23. Question 26 Twnty-nine executives reported the number of telephone calls made during a randomly selected week as shown here. 24 15 12 8 56 12 18 12 15 43 10 15 5 22 36 29 35 24 8 33 58 32 46 19 7 16 26 29 53 Find the mean, median and mode. Find the 42th percentile P42 .
Question 1 Consider the following questions being asked on a survey. What is the measurement scale of the response data? (a) Ordinal (b)Nominal (c) Interval (d)Ratio – Discrete (e) Ratio - Continuous 1) What was the rating of the hotel that you last stayed in? a) Dissatisfied b) Somewhat Dissatisfied c) Somewhat satisfied d) Satisfied e) Very good 2) What is your marital status? 1=Married; 2=Common Law; 3=Widowed; 4=Divorced; 5=Single 3) What is the major that you are studying? a) Math b) Physics c) Chemistry d) Biology e) History 4) What is the postal code? 5) Which letter grade did you get on your Chemistry course last term? 6) What is the color of your eyes? 7) What is the color of your car? 8) Where is your hometown? 9) How many courses are taking this term? 10) How much time do you spend on shopping each week? 11) What was the lowest temperature in 0 C in the city you are living last month? 12) How many children do you intend to have? 13) How many languages can you speak? 14) Which language is your native language? 15) Where were you born? 16) What is your weight? 17) How long does it take for you to walk from your home to Ryerson?
NOTE: Questions 2 – 3 are based on the following information.
The following data represents the heights (m) for a sample of 11 boys at age 12. 1.38, 1.43, 1.25, 1.47, 1.29, 1.54, 1.37, 1.25, 1.53, 1.45, 1.29 Question 2 If you were to construct a stem-and-leaf display using the rules discussed in lectures for the above data, how many stems should your stem-and-leaf display have? a) 7 b) 8 c) 6 d) 9 e) None of these Question 3 Based on the stem-and-leaf display (using the rules discussed in lectures) for the above data, how many leaves would there be on the second stem of your stem-and-leaf display? a) 4 b) 0 c) 2 d) 3 e) None of these NOTE: Questions 4 - 7 are based on the following information. The following data represents the heights (m) for a sample of 12 boys at age 12. 1.38, 1.43, 1.25, 1.47, 1.29, 1.54, 1.37, 1.25, 1.53, 1.45, 1.29, 1.41 Question 4 If you were to construct a frequency distribution using the rules discussed in lectures for the above data, what would the class width (in thousand dollars) be? a) 1.0 b) 0.05 c) 0.50 d) 0.10 e) 0.025 Question 5 If you were to construct a frequency distribution using the rules discussed in lectures for the above data, how many classes are there in the frequency distribution? a) 4 b) 5 c) 8 d) 6 e) 10 Question 6 Based on the frequency distribution using the rules discussed in lectures for the above data, what is the relative frequency of the fourth class? (The answers provided below are rounded to three decimal places). a) 0.250 b) 0.333 c) 0.375 d) 0.167 e) None of these Question 7 Based on the frequency distribution using the rules discussed in lectures for the above data, what is the cumulative percentage of up to and including the third class? (The answers provided below are rounded to two decimal places). a) 16.67% b) 33.33% c) 50.00% d) 46.67% e) None of these
Use the following data for questions 8 to 10 inclusive.
The following table represents the distribution of the income ($1000) in 2011 for a sample of households in Toronto. Table 1 Income ($1000) Number of households 20 and under 37 30 30 and under 22 40 40 and under 45 50 50 and under 5 60 60 and under 20 70 70 and under 11 80 80 and under 15 90 Question 8 The number households in this sample, whose incomes in 2011 are lower than $70,000, is a) 12.9% b) 16.8% c) 73.5% d) 83.2% e) 80.3%
Question 9 The relative frequency of the households in this sample, whose incomes in 2011 are higher than $50,000, is (rounded to three decimal places): a) 0.671 b) 0.032 c) 0.329 d) Cannot be determined from the table e) None of the above Question 10 The class width (in $1000) for the classes in this table is: a) 10,000 b) 5,000 c) 10 d) 5
e) 25
Note: Questions 11-13 are based on the following information Forty-five students wrote the PCS105 midterm test last week. The following stem-and-leaf display shows the grades of students who failed PCS105 midterm test last week. Stem
Leaf
( ×10 ) 0 1 1 2 2 3 3 4
78 012 59 00 556 89 13
Question 11 What is the maximum value in the above data? a) 40.3 b) 4.3 c) 4.03 d) 43
e) 41.3
Question 12 How many students passed the last week’s PCS105 midterm test? a) 15 b) 16 c) 23 d) 29 e) 25 Question 13 What is the failure rate of this test? a) 64.44% b) 35.56% c) 25.72%
d) 24.73%
e) 14.32%
Note: Questions 14 – 17 are based on the following Ogive.
The length of stay, t days, that each of 500 guests stayed at a five star hotel was recorded and the results used to construct the Ogive below. Note that the first class is “0 and under 5” and the last class is “35 and under 40”.
Question 14 How many guests have stayed in this hotel at least 20 days? a) 300 b) 200 c) 150 d) 350
e) 100
Question 15 How many guests (in percentage) stayed in this hotel 15 days or less? a) 40% b) 60% c) 70% d) 35% e) cannot be determined Question 16 Find the approximate average length of stay per guest. a) 18 b) 19 c) 19.5 d) 18.5
e) cannot be answered
Question 17 Find the 70th percentile: a) 35 b) 25
e) cannot be answered
c) 15
d) 22.5
Question 18 is based the following information. The answer is rounded to one decimal place. Forty-five students wrote the PCS105 midterm test last week. The following stem-and-leaf display shows the grades of students who failed PCS105 midterm test last week. Stem ( ×10 ) 0
Leaf 78
1 1 2 2 3 3 4
012 59 00 556 89 13
Question 18 The 75th percentile of the above data is: a. 26 b. 38 c. 32 d. 25.5
e. 36.5
Use the following data for Question 19. Question 19 The following table shows some data regarding the top 5 grocery chains in Toronto. Table 1 Chains A B C D E
Number of Stores 33 21 25 12 25
Annual Revenue per store($000) 69800 42980 38900 28905 54300
Total Profit ($Million) 22 15 19 12 26
a) What is the overall mean annual revenue per store for the five chains shown? b) What is the overall mean profit per store? c) What is the overall mean profit per chain for the five chains shown? Question 20
Question 21 Construct a bar chart that represents the data in Question 20.
Question 22 Twnty-nine executives reported the number of telephone calls made during a randomly selected week as shown here. Construct a stem-and-leaf plot. 24 5 7
15 22 16
12 8 56 12 18 36 29 35 24 8 26 29 53
12 33
15 58
43 32
10 15 46 19
Question 23 Twnty-nine executives reported the number of telephone calls made during a randomly selected week as shown here. 24 15 12 8 56 12 18 12 15 43 10 15 5 22 36 29 35 24 8 33 58 32 46 19 7 16 26 29 53 Construct a frequency distribution.
Question 24 Construct a relative frequency distribution from the data in Question 23. Question 25 Construct a cumulative frequency distribution from the data in Question 23. Question 26 Twnty-nine executives reported the number of telephone calls made during a randomly selected week as shown here. 24 15 12 8 56 12 18 12 15 43 10 15 5 22 36 29 35 24 8 33 58 32 46 19 7 16 26 29 53 Find the mean, median and mode. Find the 42th percentile P42 .
