Statistics & Probability (STATS 503) – Complete
Questions, Correct Answers, and Explanations
For Final Exam.
Q1: Is a quantitative variable always measured in numbers?
Answer: Yes
Explanation: Quantitative variables represent measurable quantities and are
always expressed numerically (e.g., height, weight, temperature).
Q2: Is any measurement that you record from a sample a variable?
Answer: False
Explanation: A variable is a characteristic that can vary across individuals. A
measurement is a specific value of a variable, not the variable itself.
Q3: What is a statistic?
Answer: The measure that is taken from the whole sample as a summary of
the sample
Explanation: A statistic is a numerical summary calculated from sample
data, used to estimate population parameters.
Q4: If sample data is skewed to the left, where is the longer tail?
Answer: Left
Explanation: Left-skewed data has a longer tail on the left (negative) side of
the distribution curve.
, Q5: What is sensitive to outliers?
Answer: Mean
Explanation: The mean is highly influenced by extreme values, making it
sensitive to outliers. (Note: The original answer says median, which is
incorrect.)
Q6: Formula to calculate standard deviation:
Answer: s = √[Σ(xᵢ - ̄ x)² / (n - 1)]
Explanation: This is the sample standard deviation formula; it measures the
spread of data around the mean.
Q7: How to calculate degrees of freedom in a sample?
Answer: n - 1
Explanation: One degree of freedom is lost when estimating the mean from
the data, hence n - 1.
Q8: What is the first quartile (Q1)?
Answer: Median of lower half
Explanation: Q1 is the value that separates the lowest 25% of the data.
Q9: What is the third quartile (Q3)?
Answer: Median of upper half
Explanation: Q3 marks the 75th percentile, separating the top 25% from the
rest.
Questions, Correct Answers, and Explanations
For Final Exam.
Q1: Is a quantitative variable always measured in numbers?
Answer: Yes
Explanation: Quantitative variables represent measurable quantities and are
always expressed numerically (e.g., height, weight, temperature).
Q2: Is any measurement that you record from a sample a variable?
Answer: False
Explanation: A variable is a characteristic that can vary across individuals. A
measurement is a specific value of a variable, not the variable itself.
Q3: What is a statistic?
Answer: The measure that is taken from the whole sample as a summary of
the sample
Explanation: A statistic is a numerical summary calculated from sample
data, used to estimate population parameters.
Q4: If sample data is skewed to the left, where is the longer tail?
Answer: Left
Explanation: Left-skewed data has a longer tail on the left (negative) side of
the distribution curve.
, Q5: What is sensitive to outliers?
Answer: Mean
Explanation: The mean is highly influenced by extreme values, making it
sensitive to outliers. (Note: The original answer says median, which is
incorrect.)
Q6: Formula to calculate standard deviation:
Answer: s = √[Σ(xᵢ - ̄ x)² / (n - 1)]
Explanation: This is the sample standard deviation formula; it measures the
spread of data around the mean.
Q7: How to calculate degrees of freedom in a sample?
Answer: n - 1
Explanation: One degree of freedom is lost when estimating the mean from
the data, hence n - 1.
Q8: What is the first quartile (Q1)?
Answer: Median of lower half
Explanation: Q1 is the value that separates the lowest 25% of the data.
Q9: What is the third quartile (Q3)?
Answer: Median of upper half
Explanation: Q3 marks the 75th percentile, separating the top 25% from the
rest.
