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Business Statistics I QMS102 - Test 1 REVIEW PROBLEMS
Question 1 In a survey the respondent is asked to report the amount of income tax paid in 2010. The scale of measurement used is: a) Nominal b) Interval c) Ratio d) Ordinal e) None of the above Question 2 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? Ordinal a) Dissatisfied b) Somewhat Dissatisfied c) Somewhat satisfied d) Satisfied e) Very good 2) What is your marital status? Nominal 1=Married; 2=Common Law; 3=Widowed; 4=Divorced; 5=Single 3) What is the major that you are studying? Nominal a) Math b) Physics c) Chemistry d) Biology e) History 4) What is the postal code? Nominal 5) Which letter grade did you get on your Chemistry course last term? Ordinal 6) What is the color of your eyes? Nominal 7) What is the color of your car? Nominal 8) Where is your hometown? Nominal 9) How many courses are taking this term? Ratio – Discrete 10) How much time do you spend on shopping each week? Ratio - Continuous 11) What was the lowest temperature in 0 C in the city you are living last month? Interval 12) How many children do you intend to have? Ratio – Discrete 13) How many languages can you speak? Ratio – Discrete 14) Which language is your native language? Nominal 15) Where were you born? Nominal
16) What is your weight? Ratio - Continuous 17) How long does it take for you to walk from your home to Ryerson? Ratio Continuous NOTE: Questions 3 – 4 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 3 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 final stem-and-leaf display have? a) 7 b) 8 c) 6 d) 9 e) None of these Question 4 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 5 - 8 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 5 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 6 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 7 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 8 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 9 to 11 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 9 The cumulative relative frequency of the 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 10 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 11 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 12-14 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 ( ×10 ) 0 1 1 2 2 3 3 4
Leaf 78 012 59 00 556 89 13
Question 12 What is the maximum value in the above data? a) 40.3 b) 4.3 c) 4.03 d) 43
e) 41.3
Question 13 How many students passed the last week’s PCS105 midterm test? a) 15 b) 16 c) 23 d) 29 e) 25 Question 14 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 15 – 18 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 15 How many guests have stayed in this hotel at least 20 days? a) 300 b) 200 c) 150 d) 350
e) 100
Question 16 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 17 Find the approximate average length of stay per guest. a) 18 b) 19 c) 19.5 d) 18.5 Question 18 Find the 70th percentile: a) 35 b) 25 c) 15 d) 22.5
e) cannot be answered e) cannot be answered
Question 19 Listed below are the annual union fees paid by a simple random sample of Ryersonians. $400, $383.5, $350.7, $232.5, $360, $1102.43, $421, $810.09, $122.33. What is the coefficient of variation of the above data? (Rounded to two decimal places) a. 65.17% b. 61.44 c. 65.17 d. 61.44%
e. 63.45% Question 20 Listed below are the annual union fees paid by a simple random sample of Ryersonians. $400, $383.5, $350.7, $232.5, $360, $1102.43, $421, $810.09, $122.33. What is the variance of the above data? (Rounded to two decimal places) a. 81530.81 b. 66754.44 c. 91721.76 d. 285.54 e. 302.86 Questions 21-22 are based the following information. The answers are 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 1 1 2 2 3 3 4
Leaf 78 012 59 00 556 89 13
Question 21 The 75th percentile of the above data is: a. 26 b. 38 c. 32 d. 25.5
Question 22 The range of the above data is: a. 20.5 b. 35 c. 26
d. 25
e. 36.5
e. 15
Use the following data for Question 23. Question 23 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? (50714.14 thousand dollars) b) What is the standard deviation of the annual revenue per store? (14079.14 thousand dollars) c) What is the overall mean profit per store? (0.81 Million dollars) d) What is the overall mean profit per chain for the five chains shown? (18.8 Million dollars) e) What is the standard deviation of the profit per chain? (5.54 Million dollars)
Question 24
Answer is B
Question 25 Construct a bar chart that represents the data in Question 24.
Question 26 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 Stem ( ×10 ) 0 1 1 2 2 3 3 4 4 5 5
12 33
15 58
43 32
10 15 46 19
Leaf 5788 0222 555689 244 699 23 56 3 6 3 68
Question 27 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. Key answer: Class 0 and under 10 10 and under 20 20 and under 30 30 and under 40 40 and under 50 50 and under 60
Frequency 4 10 6 4 2 3
Question 28 Construct a relative frequency distribution from the data in Question 27. Class 0 and under 10 10 and under 20 20 and under 30 30 and under 40 40 and under 50 50 and under 60
Relative Frequency 0.138 0.345 0.207 0.138 0.069 0.103
Question 29 Construct a cumulative frequency distribution from the data in Question 27. Class 0 and under 10 10 and under 20 20 and under 30 30 and under 40 40 and under 50 50 and under 60
Cumulative Frequency 4 14 20 24 26 29
Question 30 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. Mean=24.76 Median=22 Mode=12, 15
P42 = 12 ( x12 + x13 ) = 12 (16 + 18) = 17
Question 1 In a survey the respondent is asked to report the amount of income tax paid in 2010. The scale of measurement used is: a) Nominal b) Interval c) Ratio d) Ordinal e) None of the above Question 2 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? Ordinal a) Dissatisfied b) Somewhat Dissatisfied c) Somewhat satisfied d) Satisfied e) Very good 2) What is your marital status? Nominal 1=Married; 2=Common Law; 3=Widowed; 4=Divorced; 5=Single 3) What is the major that you are studying? Nominal a) Math b) Physics c) Chemistry d) Biology e) History 4) What is the postal code? Nominal 5) Which letter grade did you get on your Chemistry course last term? Ordinal 6) What is the color of your eyes? Nominal 7) What is the color of your car? Nominal 8) Where is your hometown? Nominal 9) How many courses are taking this term? Ratio – Discrete 10) How much time do you spend on shopping each week? Ratio - Continuous 11) What was the lowest temperature in 0 C in the city you are living last month? Interval 12) How many children do you intend to have? Ratio – Discrete 13) How many languages can you speak? Ratio – Discrete 14) Which language is your native language? Nominal 15) Where were you born? Nominal
16) What is your weight? Ratio - Continuous 17) How long does it take for you to walk from your home to Ryerson? Ratio Continuous NOTE: Questions 3 – 4 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 3 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 final stem-and-leaf display have? a) 7 b) 8 c) 6 d) 9 e) None of these Question 4 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 5 - 8 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 5 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 6 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 7 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 8 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 9 to 11 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 9 The cumulative relative frequency of the 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 10 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 11 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 12-14 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 ( ×10 ) 0 1 1 2 2 3 3 4
Leaf 78 012 59 00 556 89 13
Question 12 What is the maximum value in the above data? a) 40.3 b) 4.3 c) 4.03 d) 43
e) 41.3
Question 13 How many students passed the last week’s PCS105 midterm test? a) 15 b) 16 c) 23 d) 29 e) 25 Question 14 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 15 – 18 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 15 How many guests have stayed in this hotel at least 20 days? a) 300 b) 200 c) 150 d) 350
e) 100
Question 16 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 17 Find the approximate average length of stay per guest. a) 18 b) 19 c) 19.5 d) 18.5 Question 18 Find the 70th percentile: a) 35 b) 25 c) 15 d) 22.5
e) cannot be answered e) cannot be answered
Question 19 Listed below are the annual union fees paid by a simple random sample of Ryersonians. $400, $383.5, $350.7, $232.5, $360, $1102.43, $421, $810.09, $122.33. What is the coefficient of variation of the above data? (Rounded to two decimal places) a. 65.17% b. 61.44 c. 65.17 d. 61.44%
e. 63.45% Question 20 Listed below are the annual union fees paid by a simple random sample of Ryersonians. $400, $383.5, $350.7, $232.5, $360, $1102.43, $421, $810.09, $122.33. What is the variance of the above data? (Rounded to two decimal places) a. 81530.81 b. 66754.44 c. 91721.76 d. 285.54 e. 302.86 Questions 21-22 are based the following information. The answers are 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 1 1 2 2 3 3 4
Leaf 78 012 59 00 556 89 13
Question 21 The 75th percentile of the above data is: a. 26 b. 38 c. 32 d. 25.5
Question 22 The range of the above data is: a. 20.5 b. 35 c. 26
d. 25
e. 36.5
e. 15
Use the following data for Question 23. Question 23 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? (50714.14 thousand dollars) b) What is the standard deviation of the annual revenue per store? (14079.14 thousand dollars) c) What is the overall mean profit per store? (0.81 Million dollars) d) What is the overall mean profit per chain for the five chains shown? (18.8 Million dollars) e) What is the standard deviation of the profit per chain? (5.54 Million dollars)
Question 24
Answer is B
Question 25 Construct a bar chart that represents the data in Question 24.
Question 26 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 Stem ( ×10 ) 0 1 1 2 2 3 3 4 4 5 5
12 33
15 58
43 32
10 15 46 19
Leaf 5788 0222 555689 244 699 23 56 3 6 3 68
Question 27 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. Key answer: Class 0 and under 10 10 and under 20 20 and under 30 30 and under 40 40 and under 50 50 and under 60
Frequency 4 10 6 4 2 3
Question 28 Construct a relative frequency distribution from the data in Question 27. Class 0 and under 10 10 and under 20 20 and under 30 30 and under 40 40 and under 50 50 and under 60
Relative Frequency 0.138 0.345 0.207 0.138 0.069 0.103
Question 29 Construct a cumulative frequency distribution from the data in Question 27. Class 0 and under 10 10 and under 20 20 and under 30 30 and under 40 40 and under 50 50 and under 60
Cumulative Frequency 4 14 20 24 26 29
Question 30 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. Mean=24.76 Median=22 Mode=12, 15
P42 = 12 ( x12 + x13 ) = 12 (16 + 18) = 17
