Sophia Introduction to Statistics Final Milestone:
Questions and Answers with Graded Solutions
Section 1: Types of Data & Descriptive Statistics (5
Questions)
1. Types of Data
A researcher records the number of pets owned by households in a neighborhood. This is an
example of: A) Qualitative data B) Continuous quantitative data C) Discrete quantitative data
D) Nominal data
Correct Answer: C) Discrete quantitative data Rationale:
● Discrete data consists of countable, whole numbers (e.g., number of pets).
● Continuous data can take any value within a range (e.g., height, weight).
● Qualitative data is categorical (e.g., pet type: dog, cat).
● Nominal data is a type of qualitative data with no inherent order.
2. Descriptive Statistics: Mean vs. Median
A dataset has the following values: 3, 5, 7, 9, 12, 15, 100. Which measure of central tendency is
most affected by the outlier (100)? A) Median B) Mean C) Mode D) Range
Correct Answer: B) Mean Rationale:
● The mean is highly sensitive to outliers because it uses all values in its calculation.
● The median (7th value in ordered list: 9) is resistant to outliers.
● The mode is the most frequent value (none here).
● The range is affected by outliers but is a measure of spread, not central tendency.
3. Standard Deviation
, A dataset has a mean of 50 and a standard deviation of 5. What does the standard deviation
represent? A) The average distance of data points from the median B) The average distance
of data points from the mean C) The range of the dataset D) The interquartile range (IQR)
Correct Answer: B) The average distance of data points from the mean Rationale:
● Standard deviation measures the spread of data around the mean.
● It is not the range or IQR, which are other measures of spread.
4. Interquartile Range (IQR)
The IQR of a dataset is 12. The first quartile (Q1) is 20. What is the third quartile (Q3)? A) 8
B) 20 C) 32 D) 44
Correct Answer: C) 32 Rationale:
● IQR = Q3 – Q1
● 32 = 20 + 12
5. Outliers
Using the 1.5 × IQR rule , a dataset has:
● Q1 = 10
● Q3 = 20
● IQR = 10 What is the upper boundary for outliers? A) 25 B) 35 C) 40 D) 50
Correct Answer: B) 35 Rationale:
● Upper boundary = Q3 + 1.5 × IQR = 20 + 1.5(10) = 35
Section 2: Probability (5 Questions)
6. Independent Events
If P(A) = 0.4 and P(B) = 0.3, and A and B are independent, what is P(A and B)? A) 0.07 B) 0.12
C) 0.25 D) 0.7
Correct Answer: B) 0.12 Rationale:
Questions and Answers with Graded Solutions
Section 1: Types of Data & Descriptive Statistics (5
Questions)
1. Types of Data
A researcher records the number of pets owned by households in a neighborhood. This is an
example of: A) Qualitative data B) Continuous quantitative data C) Discrete quantitative data
D) Nominal data
Correct Answer: C) Discrete quantitative data Rationale:
● Discrete data consists of countable, whole numbers (e.g., number of pets).
● Continuous data can take any value within a range (e.g., height, weight).
● Qualitative data is categorical (e.g., pet type: dog, cat).
● Nominal data is a type of qualitative data with no inherent order.
2. Descriptive Statistics: Mean vs. Median
A dataset has the following values: 3, 5, 7, 9, 12, 15, 100. Which measure of central tendency is
most affected by the outlier (100)? A) Median B) Mean C) Mode D) Range
Correct Answer: B) Mean Rationale:
● The mean is highly sensitive to outliers because it uses all values in its calculation.
● The median (7th value in ordered list: 9) is resistant to outliers.
● The mode is the most frequent value (none here).
● The range is affected by outliers but is a measure of spread, not central tendency.
3. Standard Deviation
, A dataset has a mean of 50 and a standard deviation of 5. What does the standard deviation
represent? A) The average distance of data points from the median B) The average distance
of data points from the mean C) The range of the dataset D) The interquartile range (IQR)
Correct Answer: B) The average distance of data points from the mean Rationale:
● Standard deviation measures the spread of data around the mean.
● It is not the range or IQR, which are other measures of spread.
4. Interquartile Range (IQR)
The IQR of a dataset is 12. The first quartile (Q1) is 20. What is the third quartile (Q3)? A) 8
B) 20 C) 32 D) 44
Correct Answer: C) 32 Rationale:
● IQR = Q3 – Q1
● 32 = 20 + 12
5. Outliers
Using the 1.5 × IQR rule , a dataset has:
● Q1 = 10
● Q3 = 20
● IQR = 10 What is the upper boundary for outliers? A) 25 B) 35 C) 40 D) 50
Correct Answer: B) 35 Rationale:
● Upper boundary = Q3 + 1.5 × IQR = 20 + 1.5(10) = 35
Section 2: Probability (5 Questions)
6. Independent Events
If P(A) = 0.4 and P(B) = 0.3, and A and B are independent, what is P(A and B)? A) 0.07 B) 0.12
C) 0.25 D) 0.7
Correct Answer: B) 0.12 Rationale:
