Question 1
The two branches of the study of statistics are generally referred to as
A) descriptive and inferential statistics.
B) inferential and differential statistics.
C) descriptive and referential statistics.
D) differential and descriptive statistics.
Answer: A) descriptive and inferential statistics
Explanation:
Statistics has two main areas:
Descriptive statistics → summarize data (mean, median, graphs)
Inferential statistics → make conclusions about populations from samples
Question 2
Population parameters are difficult to calculate due to
A) cost prohibitions on data collection.
B) the infeasibility of collecting data on the entire population.
C) the fact that samples are difficult to draw due to the nature of the data.
D) both cost prohibitions on data collection and the infeasibility of collecting data on the entire population.
Answer: D) both cost prohibitions on data collection and the infeasibility of collecting data on the entire population
Explanation:
Collecting data from an entire population is:
Expensive
Often impossible
Question 3
In inferential statistics, we calculate statistics of sample data to
A) estimate unknown population parameters.
B) conduct tests about unknown population parameters.
C) Both of these choices are correct.
D) Neither of these choices is correct.
Answer: C) Both of these choices are correct
Explanation:
Inferential statistics is used to:
Estimate parameters (like population mean)
Perform hypothesis testing
Question 4
Which of the following represents a population and a sample from that population?
A) Attendees at a sporting event, and those who purchased popcorn at said sporting event
B) Full-time employees at a marketing firm, and temporary summer interns at the marketing firm
C) Seniors at Boston College and students in a first-semester business statistics course
D) Stocks available on the NYSE and stocks on the NASDAQ
Answer: A)
Explanation:
Population = all attendees
Sample = subset (those who bought popcorn)
Other options are not subsets.
Question 5
A city in California spent $15 million repairing damage to its public buildings in Year 1. The following table shows the categories where the money was directed.
Cause | Percent
Termites 30%
Water Damage 4%
Mold 11%
Earthquake 26%
Other 29%
How much did the city spend to fix damage caused by Mold?
A) $1,650,000
B) $3,300,000
C) $4,500,000
D) $825,000
Answer: A) $1,650,000
Step-by-step calculation:
1. Total spending = $15,000,000
2. Mold percentage = 11% = 0.11
3. Multiply:
15,000,000 × 0.11=1,650,000
Question 6
Which of the following best describes a frequency distribution for a categorical variable?
A) It groups data into histograms and records the proportion (fraction) of observations in each histogram.
B) It groups data into categories and records the number of observations in each category.
C) It groups data into intervals and records the proportion (fraction) of observations in each interval.
D) It groups data into intervals and records the number of observations in each intervals.
Answer: B)
Explanation:
Categorical variables → categories (not intervals)
Frequency = counts
Question 7
An analyst constructed the following frequency distribution on the monthly returns for 59 selected stocks.
Class (in percent) | Frequency
–10 up to 0 | 14
0 up to 10 | 25
10 up to 20 | 16
20 up to 30 | 4
,The number of stocks with returns of 0% up to 10% is __________blank.
A) 25
B) 14
C) 16
D) 4
Answer: A) 25
Explanation:
Just read the table → frequency = 25
Question 8
The accompanying table shows students' scores from the final exam in a history course.
Scores | Cumulative Frequency
50 up to 60 | 11
60 up to 70 | 33
70 up to 80 | 64
80 up to 90 | 93
90 up to 100 | 100
How many of the students scored at least 70 but less than 90?
A) 93
B) 36
C) 60
D) 29
Answer: C) 60
Step-by-step:
Up to 90 → 93 students
Up to 70 → 33 students
Subtract:
93−33=60
Question 9
The following frequency distribution shows the frequency of the asking price, in thousands of dollars, for current homes on the market in a particular city.
Asking Price | Frequency
$350 up to $400 | 16
$400 up to $450 | 16
$450 up to $500 | 5
$500 up to $550 | 6
$550 up to $600 | 4
What percentage of houses has an asking price between $350,000 and under $400,000?
A) 43.1%
B) 45.5%
C) 34.0%
D) 28.6%
Answer: D) 28.6%
Step-by-step:
1. Total houses:
16+16+5+6+4=47
2. Target group = 16
3. Percentage:
16
≈ 0.340 \(Wait—check carefully!\)
47
Actually:
16 ÷ 47=0.3404=34.0 %
✔ Correct answer: C) 34.0%
Question 10
Which of the following is the most influenced by outliers?
A) Mode
B) Median
C) 75th percentile
D) Arithmetic mean
Answer: D) Arithmetic mean
Explanation:
Outliers strongly affect the mean because it uses all values.
Question 11
Is it possible for a data set to have no mode?
A) Yes, if two observations occur twice.
B) No, unless there is an odd number of observations.
C) No, if the data set is nonempty, there is always a mode.
D) Yes, if there are no observations that occur more frequently than others.
Answer: D) Yes, if there are no observations that occur more frequently than others.
Explanation:
A mode is the most frequent value.
If all values occur equally → no mode exists.
Question 12
The Boom company has recently decided to raise the salaries of all employees by 10%. Which of the following is (are) expected to be affected by this raise?
A) Mean and mode only
B) Mean and median only
C) Mode and median only
D) Mean, median, and mode
Answer: D) Mean, median, and mode
Explanation:
Every value increases → all measures of central tendency increase.
Question 13
, The owner of a small company has recently decided to raise the salary of one employee, who was already making the highest salary, by 20%. Which of the following is(are) expected to be affected
by this raise?
A) Mean only
B) Median only
C) Mean and median only
D) Mean, median, and mode
Answer: A) Mean only
Explanation:
Only the largest value changes
Mean changes (uses all values)
Median stays same (middle value unchanged)
Mode unchanged unless that value was the most frequent
Question 14
A college professor collected data on the number of hours spent by his 100 students over the weekend to prepare for Monday’s Business Statistics exam. He processed the data by Excel and the
following incomplete output is available.
Mean = 13
Sample Variance = 6.79
Skewness = 1.03
The median is most likely to be __________blank.
A) about 13 hours
B) less than 13 hours
C) greater than 13 hours
D) Cannot tell from the information provided
Answer: B) less than 13 hours
Explanation:
Skewness = positive (1.03) → right-skewed distribution
In right-skewed data:
Mean > Median
So median < 13
Question 15
Which of the following is true when using the empirical rule (if applicable) for a sample data?
A) Almost all observations are in the interval
B) Approximately 68% of all observations are in the interval
C) Approximately 95% of all observations are in the interval
D) Approximately 68% of all observations are in the interval
Answer: B) Approximately 68% of all observations are in the interval
Explanation:
Empirical Rule:
68% → within 1 standard deviation
95% → within 2
99.7% → within 3
Question 16
When using the empirical rule, which of the following assumptions is made?
A) The data only come from a sample.
B) The data only come from a population.
C) The data are exactly symmetric and bell-shaped.
D) The data are relatively symmetric and bell-shaped.
Answer: D) The data are relatively symmetric and bell-shaped.
Explanation:
Empirical rule applies to approximately normal distributions, not perfect ones.
Question 17
In an accounting class of 200 students, the mean and standard deviation of scores were 70 and 5, respectively. Assume the scores’ distribution was relatively symmetric and bell-shaped. Use the
empirical rule to determine the number of students who scored less than 65 or more than 75.
A) Approximately 32.
B) Approximately 64.
C) Approximately 68.
D) Approximately 136.
Answer: B) Approximately 64
Step-by-step:
1. Mean = 70, SD = 5
2. Interval: 65 to 75 = mean ± 1 SD
3. Empirical rule:
68% within ±1 SD
So outside = 100% − 68% = 32%
4. Number of students:
200 × 0.32=64
Question 18
You buy 50 stocks of Company A, 30 of Company B, and 20 of Company C. The annual returns of these companies are 8%, 12%, and 10% respectively. The average return for one year is the
closest to __________.
A) 9.1%
B) 9.6%
C) 10.0%
D) 10.5%
Answer: B) 9.6%
Step-by-step (weighted average):
50( 8 )+30(12)+20(10 ) 400+360+200 960
Average= ¿ = =9.6 %
50+30+20 100 100
The two branches of the study of statistics are generally referred to as
A) descriptive and inferential statistics.
B) inferential and differential statistics.
C) descriptive and referential statistics.
D) differential and descriptive statistics.
Answer: A) descriptive and inferential statistics
Explanation:
Statistics has two main areas:
Descriptive statistics → summarize data (mean, median, graphs)
Inferential statistics → make conclusions about populations from samples
Question 2
Population parameters are difficult to calculate due to
A) cost prohibitions on data collection.
B) the infeasibility of collecting data on the entire population.
C) the fact that samples are difficult to draw due to the nature of the data.
D) both cost prohibitions on data collection and the infeasibility of collecting data on the entire population.
Answer: D) both cost prohibitions on data collection and the infeasibility of collecting data on the entire population
Explanation:
Collecting data from an entire population is:
Expensive
Often impossible
Question 3
In inferential statistics, we calculate statistics of sample data to
A) estimate unknown population parameters.
B) conduct tests about unknown population parameters.
C) Both of these choices are correct.
D) Neither of these choices is correct.
Answer: C) Both of these choices are correct
Explanation:
Inferential statistics is used to:
Estimate parameters (like population mean)
Perform hypothesis testing
Question 4
Which of the following represents a population and a sample from that population?
A) Attendees at a sporting event, and those who purchased popcorn at said sporting event
B) Full-time employees at a marketing firm, and temporary summer interns at the marketing firm
C) Seniors at Boston College and students in a first-semester business statistics course
D) Stocks available on the NYSE and stocks on the NASDAQ
Answer: A)
Explanation:
Population = all attendees
Sample = subset (those who bought popcorn)
Other options are not subsets.
Question 5
A city in California spent $15 million repairing damage to its public buildings in Year 1. The following table shows the categories where the money was directed.
Cause | Percent
Termites 30%
Water Damage 4%
Mold 11%
Earthquake 26%
Other 29%
How much did the city spend to fix damage caused by Mold?
A) $1,650,000
B) $3,300,000
C) $4,500,000
D) $825,000
Answer: A) $1,650,000
Step-by-step calculation:
1. Total spending = $15,000,000
2. Mold percentage = 11% = 0.11
3. Multiply:
15,000,000 × 0.11=1,650,000
Question 6
Which of the following best describes a frequency distribution for a categorical variable?
A) It groups data into histograms and records the proportion (fraction) of observations in each histogram.
B) It groups data into categories and records the number of observations in each category.
C) It groups data into intervals and records the proportion (fraction) of observations in each interval.
D) It groups data into intervals and records the number of observations in each intervals.
Answer: B)
Explanation:
Categorical variables → categories (not intervals)
Frequency = counts
Question 7
An analyst constructed the following frequency distribution on the monthly returns for 59 selected stocks.
Class (in percent) | Frequency
–10 up to 0 | 14
0 up to 10 | 25
10 up to 20 | 16
20 up to 30 | 4
,The number of stocks with returns of 0% up to 10% is __________blank.
A) 25
B) 14
C) 16
D) 4
Answer: A) 25
Explanation:
Just read the table → frequency = 25
Question 8
The accompanying table shows students' scores from the final exam in a history course.
Scores | Cumulative Frequency
50 up to 60 | 11
60 up to 70 | 33
70 up to 80 | 64
80 up to 90 | 93
90 up to 100 | 100
How many of the students scored at least 70 but less than 90?
A) 93
B) 36
C) 60
D) 29
Answer: C) 60
Step-by-step:
Up to 90 → 93 students
Up to 70 → 33 students
Subtract:
93−33=60
Question 9
The following frequency distribution shows the frequency of the asking price, in thousands of dollars, for current homes on the market in a particular city.
Asking Price | Frequency
$350 up to $400 | 16
$400 up to $450 | 16
$450 up to $500 | 5
$500 up to $550 | 6
$550 up to $600 | 4
What percentage of houses has an asking price between $350,000 and under $400,000?
A) 43.1%
B) 45.5%
C) 34.0%
D) 28.6%
Answer: D) 28.6%
Step-by-step:
1. Total houses:
16+16+5+6+4=47
2. Target group = 16
3. Percentage:
16
≈ 0.340 \(Wait—check carefully!\)
47
Actually:
16 ÷ 47=0.3404=34.0 %
✔ Correct answer: C) 34.0%
Question 10
Which of the following is the most influenced by outliers?
A) Mode
B) Median
C) 75th percentile
D) Arithmetic mean
Answer: D) Arithmetic mean
Explanation:
Outliers strongly affect the mean because it uses all values.
Question 11
Is it possible for a data set to have no mode?
A) Yes, if two observations occur twice.
B) No, unless there is an odd number of observations.
C) No, if the data set is nonempty, there is always a mode.
D) Yes, if there are no observations that occur more frequently than others.
Answer: D) Yes, if there are no observations that occur more frequently than others.
Explanation:
A mode is the most frequent value.
If all values occur equally → no mode exists.
Question 12
The Boom company has recently decided to raise the salaries of all employees by 10%. Which of the following is (are) expected to be affected by this raise?
A) Mean and mode only
B) Mean and median only
C) Mode and median only
D) Mean, median, and mode
Answer: D) Mean, median, and mode
Explanation:
Every value increases → all measures of central tendency increase.
Question 13
, The owner of a small company has recently decided to raise the salary of one employee, who was already making the highest salary, by 20%. Which of the following is(are) expected to be affected
by this raise?
A) Mean only
B) Median only
C) Mean and median only
D) Mean, median, and mode
Answer: A) Mean only
Explanation:
Only the largest value changes
Mean changes (uses all values)
Median stays same (middle value unchanged)
Mode unchanged unless that value was the most frequent
Question 14
A college professor collected data on the number of hours spent by his 100 students over the weekend to prepare for Monday’s Business Statistics exam. He processed the data by Excel and the
following incomplete output is available.
Mean = 13
Sample Variance = 6.79
Skewness = 1.03
The median is most likely to be __________blank.
A) about 13 hours
B) less than 13 hours
C) greater than 13 hours
D) Cannot tell from the information provided
Answer: B) less than 13 hours
Explanation:
Skewness = positive (1.03) → right-skewed distribution
In right-skewed data:
Mean > Median
So median < 13
Question 15
Which of the following is true when using the empirical rule (if applicable) for a sample data?
A) Almost all observations are in the interval
B) Approximately 68% of all observations are in the interval
C) Approximately 95% of all observations are in the interval
D) Approximately 68% of all observations are in the interval
Answer: B) Approximately 68% of all observations are in the interval
Explanation:
Empirical Rule:
68% → within 1 standard deviation
95% → within 2
99.7% → within 3
Question 16
When using the empirical rule, which of the following assumptions is made?
A) The data only come from a sample.
B) The data only come from a population.
C) The data are exactly symmetric and bell-shaped.
D) The data are relatively symmetric and bell-shaped.
Answer: D) The data are relatively symmetric and bell-shaped.
Explanation:
Empirical rule applies to approximately normal distributions, not perfect ones.
Question 17
In an accounting class of 200 students, the mean and standard deviation of scores were 70 and 5, respectively. Assume the scores’ distribution was relatively symmetric and bell-shaped. Use the
empirical rule to determine the number of students who scored less than 65 or more than 75.
A) Approximately 32.
B) Approximately 64.
C) Approximately 68.
D) Approximately 136.
Answer: B) Approximately 64
Step-by-step:
1. Mean = 70, SD = 5
2. Interval: 65 to 75 = mean ± 1 SD
3. Empirical rule:
68% within ±1 SD
So outside = 100% − 68% = 32%
4. Number of students:
200 × 0.32=64
Question 18
You buy 50 stocks of Company A, 30 of Company B, and 20 of Company C. The annual returns of these companies are 8%, 12%, and 10% respectively. The average return for one year is the
closest to __________.
A) 9.1%
B) 9.6%
C) 10.0%
D) 10.5%
Answer: B) 9.6%
Step-by-step (weighted average):
50( 8 )+30(12)+20(10 ) 400+360+200 960
Average= ¿ = =9.6 %
50+30+20 100 100
