STATISTICS BEC1 Statistics Final Exam Solutions WGU (100% Complete)
Question 1
A financial analyst is studying the annual income of a population where a few billionaires cause
the distribution to be heavily skewed to the right. Which measure of central tendency would
provide the most accurate representation of a "typical" income?
A) Mean
B) Median
C) Mode
D) Range
E) Standard Deviation
Correct Answer: B) Median
Rationale: The median is the middle value in a dataset and is resistant to the effects of
extreme outliers. In a right-skewed distribution like income, the mean is pulled upward by
the high values (the billionaires), making it an inflated and less representative measure of
the typical person's income. The median provides a better measure of the center.
Question 2
A quality control manager measures the weight of 100 bags of flour. The calculation of the
average dispersion of the weights around the mean is known as the:
A) Variance
B) Interquartile Range (IQR)
C) Range
D) Standard Deviation
E) Mean
Correct Answer: D) Standard Deviation
Rationale: The standard deviation is the most common measure of the spread or dispersion
of data points in a dataset. It quantifies the average amount of variation or deviation from
the mean, providing insight into the consistency of the data.
Question 3
In a perfectly symmetrical, bell-shaped distribution, which of the following statements is true?
A) The mean is greater than the median.
B) The median is greater than the mean.
,[Type here]
C) The mean, median, and mode are all equal.
D) The distribution is skewed to the left.
E) The interquartile range is equal to the mean.
Correct Answer: C) The mean, median, and mode are all equal.
Rationale: A key characteristic of a normal (or any perfectly symmetrical) distribution is
that the three measures of central tendency—mean, median, and mode—all coincide at the
center of the distribution.
Question 4
A data analyst creates a box plot to visualize a dataset. The "box" portion of the plot represents
which part of the data?
A) The entire range of the data.
B) The data falling within one standard deviation of the mean.
C) The middle 50% of the data, between the first and third quartiles.
D) Only the outliers in the dataset.
E) The mean and the mode.
Correct Answer: C) The middle 50% of the data, between the first and third quartiles.
Rationale: A box plot is based on the five-number summary. The box itself is drawn from
the first quartile (Q1, the 25th percentile) to the third quartile (Q3, the 75th percentile).
The length of this box is the Interquartile Range (IQR) and represents the spread of the
central half of the data.
Question 5
A researcher calculates the average age of a sample of 500 customers. This calculated average is
an example of a:
A) Parameter
B) Population
C) Statistic
D) Variable
E) Census
, [Type here]
Correct Answer: C) Statistic
Rationale: A statistic is a numerical characteristic or measure calculated from a sample of
data. A parameter, in contrast, is a numerical characteristic of an entire population, which
is often what statistics are used to estimate.
Question 6
If the probability of a company's stock price increasing tomorrow is 0.7, what is the probability
that the stock price will not increase?
A) 0.7
B) 0.3
C) 0.5
D) 1.0
E) 0
Correct Answer: B) 0.3
Rationale: This is the complement rule in probability. The probability of an event not
occurring is 1 minus the probability that it will occur. P(Not A) = 1 - P(A). Therefore, 1 - 0.7
= 0.3.
Question 7
If drawing a red card and drawing a king from a standard deck of 52 cards are two events, what
is P(Red or King)?
A) 30/52
B) 28/52
C) 32/52
D) 26/52
E) 4/52
Correct Answer: B) 28/52
Rationale: This uses the addition rule for non-mutually exclusive events: P(A or B) = P(A) +
P(B) - P(A and B). P(Red) = 26/52. P(King) = 4/52. P(Red and King) = 2/52 (King of Hearts,
King of Diamonds). So, (26/52) + (4/52) - (2/52) = 28/52.
Question 1
A financial analyst is studying the annual income of a population where a few billionaires cause
the distribution to be heavily skewed to the right. Which measure of central tendency would
provide the most accurate representation of a "typical" income?
A) Mean
B) Median
C) Mode
D) Range
E) Standard Deviation
Correct Answer: B) Median
Rationale: The median is the middle value in a dataset and is resistant to the effects of
extreme outliers. In a right-skewed distribution like income, the mean is pulled upward by
the high values (the billionaires), making it an inflated and less representative measure of
the typical person's income. The median provides a better measure of the center.
Question 2
A quality control manager measures the weight of 100 bags of flour. The calculation of the
average dispersion of the weights around the mean is known as the:
A) Variance
B) Interquartile Range (IQR)
C) Range
D) Standard Deviation
E) Mean
Correct Answer: D) Standard Deviation
Rationale: The standard deviation is the most common measure of the spread or dispersion
of data points in a dataset. It quantifies the average amount of variation or deviation from
the mean, providing insight into the consistency of the data.
Question 3
In a perfectly symmetrical, bell-shaped distribution, which of the following statements is true?
A) The mean is greater than the median.
B) The median is greater than the mean.
,[Type here]
C) The mean, median, and mode are all equal.
D) The distribution is skewed to the left.
E) The interquartile range is equal to the mean.
Correct Answer: C) The mean, median, and mode are all equal.
Rationale: A key characteristic of a normal (or any perfectly symmetrical) distribution is
that the three measures of central tendency—mean, median, and mode—all coincide at the
center of the distribution.
Question 4
A data analyst creates a box plot to visualize a dataset. The "box" portion of the plot represents
which part of the data?
A) The entire range of the data.
B) The data falling within one standard deviation of the mean.
C) The middle 50% of the data, between the first and third quartiles.
D) Only the outliers in the dataset.
E) The mean and the mode.
Correct Answer: C) The middle 50% of the data, between the first and third quartiles.
Rationale: A box plot is based on the five-number summary. The box itself is drawn from
the first quartile (Q1, the 25th percentile) to the third quartile (Q3, the 75th percentile).
The length of this box is the Interquartile Range (IQR) and represents the spread of the
central half of the data.
Question 5
A researcher calculates the average age of a sample of 500 customers. This calculated average is
an example of a:
A) Parameter
B) Population
C) Statistic
D) Variable
E) Census
, [Type here]
Correct Answer: C) Statistic
Rationale: A statistic is a numerical characteristic or measure calculated from a sample of
data. A parameter, in contrast, is a numerical characteristic of an entire population, which
is often what statistics are used to estimate.
Question 6
If the probability of a company's stock price increasing tomorrow is 0.7, what is the probability
that the stock price will not increase?
A) 0.7
B) 0.3
C) 0.5
D) 1.0
E) 0
Correct Answer: B) 0.3
Rationale: This is the complement rule in probability. The probability of an event not
occurring is 1 minus the probability that it will occur. P(Not A) = 1 - P(A). Therefore, 1 - 0.7
= 0.3.
Question 7
If drawing a red card and drawing a king from a standard deck of 52 cards are two events, what
is P(Red or King)?
A) 30/52
B) 28/52
C) 32/52
D) 26/52
E) 4/52
Correct Answer: B) 28/52
Rationale: This uses the addition rule for non-mutually exclusive events: P(A or B) = P(A) +
P(B) - P(A and B). P(Red) = 26/52. P(King) = 4/52. P(Red and King) = 2/52 (King of Hearts,
King of Diamonds). So, (26/52) + (4/52) - (2/52) = 28/52.
