STAT 1000 MOCK EXAM with correct
answers and rationale
Part 1: Descriptive Statistics (Questions 1-40)
1. Which of the following is a categorical variable?
a) Height in inches
b) Number of siblings
c) Eye color
d) Temperature in Celsius
Answer: c) Eye color
Rationale: Categorical variables place individuals into groups or categories (e.g., blue, brown, green),
whereas quantitative variables take numerical values for which arithmetic operations make sense.
2. A researcher records the number of cars passing through an intersection each hour. This is an
example of:
a) A continuous variable
b) A discrete variable
c) A nominal variable
d) An ordinal variable
Answer: b) A discrete variable
Rationale: A discrete variable is a quantitative variable that has either a finite number of possible
values or a countable number of possible values. The number of cars is countable (0, 1, 2, ...).
3. The primary purpose of a histogram is to:
a) Show the relationship between two variables
b) Display the distribution of a single quantitative variable
c) Compare the frequencies of different categories
d) Identify outliers in a dataset
Answer: b) Display the distribution of a single quantitative variable
Rationale: A histogram is a graphical representation used to show the frequency distribution of
continuous or quantitative data by grouping it into bins.
4. Which measure of central tendency is most affected by extreme outliers?
a) Median
b) Mode
c) Mean
d) Range
Answer: c) Mean
Rationale: The mean is calculated by summing all values and dividing by the number of values, so an
extremely large or small value will significantly pull the mean in its direction. The median, being the
middle value, is resistant to outliers.
5. The interquartile range (IQR) is defined as:
a) The difference between the maximum and minimum values
b) The difference between the mean and the median
c) The difference between the third quartile (Q3) and the first quartile (Q1)
,d) The square root of the variance
Answer: c) The difference between the third quartile (Q3) and the first quartile (Q1)
Rationale: The IQR is a measure of spread that describes the range of the middle 50% of the data. It
is calculated as IQR = Q3 - Q1.
6. A distribution is said to be skewed to the right. Which of the following is true?
a) The mean is typically less than the median.
b) The tail of the distribution extends to the left.
c) The mean is typically greater than the median.
d) The distribution is perfectly symmetric.
Answer: c) The mean is typically greater than the median.
Rationale: A right-skewed (positively skewed) distribution has a long tail extending to the right,
which pulls the mean to the right of the median.
7. Which of the following is NOT a measure of spread?
a) Standard deviation
b) Variance
c) Median
d) Range
Answer: c) Median
Rationale: The median is a measure of central tendency, indicating the center of the data. The
range, variance, and standard deviation are all measures of spread or dispersion.
8. In a perfectly symmetric distribution, which of the following is true?
a) Mean > Median > Mode
b) Mean < Median < Mode
c) Mean = Median = Mode
d) The relationship cannot be determined.
Answer: c) Mean = Median = Mode
Rationale: In a perfectly symmetric distribution (like a normal distribution), the center of the
distribution is the same for the mean, median, and mode.
9. A student's score on a test is at the 80th percentile. This means:
a) The student answered 80% of the questions correctly.
b) The student scored higher than 80% of the other test-takers.
c) The student's score is 80 points.
d) The student scored lower than 80% of the other test-takers.
Answer: b) The student scored higher than 80% of the other test-takers.
Rationale: The kth percentile is a value such that k percent of the observations in the dataset fall at
or below that value. So, the 80th percentile is the value below which 80% of the data lies.
10. What is the primary difference between a bar chart and a histogram?
a) Bar charts are for quantitative data; histograms are for categorical data.
b) Histograms have gaps between the bars; bar charts do not.
c) Bar charts have gaps between the bars; histograms do not.
d) There is no difference.
Answer: c) Bar charts have gaps between the bars; histograms do not.
Rationale: Bar charts are used for categorical data, and the bars are drawn with gaps to show that
the categories are distinct. Histograms are for quantitative data, and the bars are adjacent to show
the continuous nature of the data.
,11. Which measure of spread is in the same units as the original data?
a) Variance
b) Standard Deviation
c) Z-score
d) Coefficient of Variation
Answer: b) Standard Deviation
Rationale: Variance is in squared units, while the standard deviation is the square root of the
variance, returning it to the original units of the data. The z-score and coefficient of variation are
unitless.
12. A list of the top 10 movies, ranked 1 to 10, is an example of what type of data?
a) Nominal
b) Ordinal
c) Interval
d) Ratio
Answer: b) Ordinal
Rationale: Ordinal data can be ordered or ranked, but the differences between the values are not
meaningful. The difference between the 1st and 2nd movie is not the same as the difference
between the 2nd and 3rd.
13. The five-number summary consists of:
a) Mean, Median, Mode, Q1, Q3
b) Min, Q1, Median, Q3, Max
c) Mean, Standard Deviation, Variance, Min, Max
d) Min, Mean, Median, Mode, Max
Answer: b) Min, Q1, Median, Q3, Max
Rationale: The five-number summary is a set of descriptive statistics that provides information
about a dataset's center and spread. It is the basis for a boxplot.
14. If a dataset has a standard deviation of 0, what can be concluded?
a) The mean is also 0.
b) All data points are the same.
c) There is a calculation error.
d) The data is normally distributed.
Answer: b) All data points are the same.
Rationale: The standard deviation measures the typical distance of data points from the mean. If it is
0, there is no variation, meaning every data point must be identical to the mean.
15. A company wants to compare the variability of salaries for two different departments with
vastly different average salaries. Which measure is most appropriate?
a) Range
b) Standard Deviation
c) Variance
d) Coefficient of Variation
Answer: d) Coefficient of Variation
Rationale: The coefficient of variation (CV = standard deviation / mean) is a relative measure of
dispersion. It is unitless and allows for the comparison of variability between datasets with different
means or units.
, 16. Which of the following is a property of the mean?
a) It is resistant to outliers.
b) It can be used for both quantitative and categorical data.
c) The sum of the deviations from the mean is always zero.
d) It is always equal to the median.
Answer: c) The sum of the deviations from the mean is always zero.
Rationale: A mathematical property of the mean is that the sum of the differences between each
data point and the mean (Σ(xi - μ)) is always equal to zero.
17. In a left-skewed distribution:
a) Mean > Median
b) Mean < Median
c) Mean = Median
d) The tail extends to the right.
Answer: b) Mean < Median
Rationale: A left-skewed (negatively skewed) distribution has a long tail to the left, which pulls the
mean to the left of the median.
18. What is the effect on the mean and median if a large outlier is added to a dataset?
a) Both the mean and median will increase significantly.
b) The mean will increase significantly, but the median will be less affected.
c) The median will increase significantly, but the mean will be less affected.
d) Neither will be affected.
Answer: b) The mean will increase significantly, but the median will be less affected.
Rationale: The mean is sensitive to every value, so an outlier will pull it strongly. The median is
resistant, as it only depends on the middle position, which may shift by only one place.
19. A z-score of -1.5 means that the data point is:
a) 1.5 standard deviations above the mean.
b) 1.5 standard deviations below the mean.
c) 1.5 times the mean.
d) 1.5 units below the mean.
Answer: b) 1.5 standard deviations below the mean.
Rationale: A z-score measures how many standard deviations a data point is from the mean. A
negative z-score indicates the value is below the mean.
20. The Empirical Rule applies to which type of distribution?
a) Any distribution
b) A right-skewed distribution
c) A left-skewed distribution
d) A bell-shaped (normal) distribution
Answer: d) A bell-shaped (normal) distribution
Rationale: The Empirical Rule (68-95-99.7 rule) is a statistical rule that states that for a normal
distribution, nearly all data will fall within three standard deviations of the mean.
21. The median is the value that:
a) Occurs most frequently.
b) Is the average of all values.
c) Divides the ordered data into two equal halves.
d) Is the difference between the largest and smallest values.
answers and rationale
Part 1: Descriptive Statistics (Questions 1-40)
1. Which of the following is a categorical variable?
a) Height in inches
b) Number of siblings
c) Eye color
d) Temperature in Celsius
Answer: c) Eye color
Rationale: Categorical variables place individuals into groups or categories (e.g., blue, brown, green),
whereas quantitative variables take numerical values for which arithmetic operations make sense.
2. A researcher records the number of cars passing through an intersection each hour. This is an
example of:
a) A continuous variable
b) A discrete variable
c) A nominal variable
d) An ordinal variable
Answer: b) A discrete variable
Rationale: A discrete variable is a quantitative variable that has either a finite number of possible
values or a countable number of possible values. The number of cars is countable (0, 1, 2, ...).
3. The primary purpose of a histogram is to:
a) Show the relationship between two variables
b) Display the distribution of a single quantitative variable
c) Compare the frequencies of different categories
d) Identify outliers in a dataset
Answer: b) Display the distribution of a single quantitative variable
Rationale: A histogram is a graphical representation used to show the frequency distribution of
continuous or quantitative data by grouping it into bins.
4. Which measure of central tendency is most affected by extreme outliers?
a) Median
b) Mode
c) Mean
d) Range
Answer: c) Mean
Rationale: The mean is calculated by summing all values and dividing by the number of values, so an
extremely large or small value will significantly pull the mean in its direction. The median, being the
middle value, is resistant to outliers.
5. The interquartile range (IQR) is defined as:
a) The difference between the maximum and minimum values
b) The difference between the mean and the median
c) The difference between the third quartile (Q3) and the first quartile (Q1)
,d) The square root of the variance
Answer: c) The difference between the third quartile (Q3) and the first quartile (Q1)
Rationale: The IQR is a measure of spread that describes the range of the middle 50% of the data. It
is calculated as IQR = Q3 - Q1.
6. A distribution is said to be skewed to the right. Which of the following is true?
a) The mean is typically less than the median.
b) The tail of the distribution extends to the left.
c) The mean is typically greater than the median.
d) The distribution is perfectly symmetric.
Answer: c) The mean is typically greater than the median.
Rationale: A right-skewed (positively skewed) distribution has a long tail extending to the right,
which pulls the mean to the right of the median.
7. Which of the following is NOT a measure of spread?
a) Standard deviation
b) Variance
c) Median
d) Range
Answer: c) Median
Rationale: The median is a measure of central tendency, indicating the center of the data. The
range, variance, and standard deviation are all measures of spread or dispersion.
8. In a perfectly symmetric distribution, which of the following is true?
a) Mean > Median > Mode
b) Mean < Median < Mode
c) Mean = Median = Mode
d) The relationship cannot be determined.
Answer: c) Mean = Median = Mode
Rationale: In a perfectly symmetric distribution (like a normal distribution), the center of the
distribution is the same for the mean, median, and mode.
9. A student's score on a test is at the 80th percentile. This means:
a) The student answered 80% of the questions correctly.
b) The student scored higher than 80% of the other test-takers.
c) The student's score is 80 points.
d) The student scored lower than 80% of the other test-takers.
Answer: b) The student scored higher than 80% of the other test-takers.
Rationale: The kth percentile is a value such that k percent of the observations in the dataset fall at
or below that value. So, the 80th percentile is the value below which 80% of the data lies.
10. What is the primary difference between a bar chart and a histogram?
a) Bar charts are for quantitative data; histograms are for categorical data.
b) Histograms have gaps between the bars; bar charts do not.
c) Bar charts have gaps between the bars; histograms do not.
d) There is no difference.
Answer: c) Bar charts have gaps between the bars; histograms do not.
Rationale: Bar charts are used for categorical data, and the bars are drawn with gaps to show that
the categories are distinct. Histograms are for quantitative data, and the bars are adjacent to show
the continuous nature of the data.
,11. Which measure of spread is in the same units as the original data?
a) Variance
b) Standard Deviation
c) Z-score
d) Coefficient of Variation
Answer: b) Standard Deviation
Rationale: Variance is in squared units, while the standard deviation is the square root of the
variance, returning it to the original units of the data. The z-score and coefficient of variation are
unitless.
12. A list of the top 10 movies, ranked 1 to 10, is an example of what type of data?
a) Nominal
b) Ordinal
c) Interval
d) Ratio
Answer: b) Ordinal
Rationale: Ordinal data can be ordered or ranked, but the differences between the values are not
meaningful. The difference between the 1st and 2nd movie is not the same as the difference
between the 2nd and 3rd.
13. The five-number summary consists of:
a) Mean, Median, Mode, Q1, Q3
b) Min, Q1, Median, Q3, Max
c) Mean, Standard Deviation, Variance, Min, Max
d) Min, Mean, Median, Mode, Max
Answer: b) Min, Q1, Median, Q3, Max
Rationale: The five-number summary is a set of descriptive statistics that provides information
about a dataset's center and spread. It is the basis for a boxplot.
14. If a dataset has a standard deviation of 0, what can be concluded?
a) The mean is also 0.
b) All data points are the same.
c) There is a calculation error.
d) The data is normally distributed.
Answer: b) All data points are the same.
Rationale: The standard deviation measures the typical distance of data points from the mean. If it is
0, there is no variation, meaning every data point must be identical to the mean.
15. A company wants to compare the variability of salaries for two different departments with
vastly different average salaries. Which measure is most appropriate?
a) Range
b) Standard Deviation
c) Variance
d) Coefficient of Variation
Answer: d) Coefficient of Variation
Rationale: The coefficient of variation (CV = standard deviation / mean) is a relative measure of
dispersion. It is unitless and allows for the comparison of variability between datasets with different
means or units.
, 16. Which of the following is a property of the mean?
a) It is resistant to outliers.
b) It can be used for both quantitative and categorical data.
c) The sum of the deviations from the mean is always zero.
d) It is always equal to the median.
Answer: c) The sum of the deviations from the mean is always zero.
Rationale: A mathematical property of the mean is that the sum of the differences between each
data point and the mean (Σ(xi - μ)) is always equal to zero.
17. In a left-skewed distribution:
a) Mean > Median
b) Mean < Median
c) Mean = Median
d) The tail extends to the right.
Answer: b) Mean < Median
Rationale: A left-skewed (negatively skewed) distribution has a long tail to the left, which pulls the
mean to the left of the median.
18. What is the effect on the mean and median if a large outlier is added to a dataset?
a) Both the mean and median will increase significantly.
b) The mean will increase significantly, but the median will be less affected.
c) The median will increase significantly, but the mean will be less affected.
d) Neither will be affected.
Answer: b) The mean will increase significantly, but the median will be less affected.
Rationale: The mean is sensitive to every value, so an outlier will pull it strongly. The median is
resistant, as it only depends on the middle position, which may shift by only one place.
19. A z-score of -1.5 means that the data point is:
a) 1.5 standard deviations above the mean.
b) 1.5 standard deviations below the mean.
c) 1.5 times the mean.
d) 1.5 units below the mean.
Answer: b) 1.5 standard deviations below the mean.
Rationale: A z-score measures how many standard deviations a data point is from the mean. A
negative z-score indicates the value is below the mean.
20. The Empirical Rule applies to which type of distribution?
a) Any distribution
b) A right-skewed distribution
c) A left-skewed distribution
d) A bell-shaped (normal) distribution
Answer: d) A bell-shaped (normal) distribution
Rationale: The Empirical Rule (68-95-99.7 rule) is a statistical rule that states that for a normal
distribution, nearly all data will fall within three standard deviations of the mean.
21. The median is the value that:
a) Occurs most frequently.
b) Is the average of all values.
c) Divides the ordered data into two equal halves.
d) Is the difference between the largest and smallest values.
