PORTAGE LEARNING MATH 110 MODULE 1
QUESTIONS AND CORRECT EXPLANATIONS
2026/2027 GRADED A+
Section A: Definitions & Key Concepts (Questions 1-15)
1. Define each of the following terms as used in statistics:
a) Observation
Correct Answer: All the information collected for each element in a study.
Rationale: In statistics, an observation is the complete set of data collected for a
single element. For example, if a study collects age, height, and weight for each
person, the set of age, height, and weight for one person constitutes one
observation. This is distinct from a single data point—it encompasses all measured
variables for that element .
b) Element
Correct Answer: In a data set, the individual and unique entry about which data
has been collected, analyzed, and presented in the same manner.
Rationale: An element (also called a "member" or "individual unit") is the
fundamental entity being studied. Each element contributes one observation to
the data set. Elements can include individual people, companies, products, or any
other distinct unit of analysis .
c) Variable
, Correct Answer: A particular, measurable attribute that the researcher believes is
needed to describe the element in their study.
Rationale: Variables are characteristics or properties that can vary among
elements in a study. Examples include age, gender, income, test scores, or blood
pressure. Variables can be either quantitative (numerical) or qualitative
(categorical) .
2. Explain what an outlier is in a data set.
Correct Answer: An outlier is a value that is out of place compared to the other
values in a data set. It may be too large or too small compared to the other
values.
Rationale: Outliers are extreme values that differ significantly from other
observations. They can occur due to measurement error, data entry errors, or
natural variation in the population. Identifying outliers is critically important
because they can heavily influence statistical measures like the mean and can
distort the results of data analysis .
3. Distinguish between descriptive and inferential statistics.
Correct Answer: Descriptive statistics involve analyses that provide a way to
summarize and describe data (e.g., mean, median, mode, standard deviation,
range). Inferential statistics are performed in order for researchers to make
inferences and generalizations about populations based on data gathered from
samples.
Rationale: Descriptive statistics help us understand what the data shows, while
inferential statistics use probability to draw conclusions about a larger population
from a smaller sample. Descriptive statistics describe; inferential statistics predict.
Both branches are essential for comprehensive data analysis .
QUESTIONS AND CORRECT EXPLANATIONS
2026/2027 GRADED A+
Section A: Definitions & Key Concepts (Questions 1-15)
1. Define each of the following terms as used in statistics:
a) Observation
Correct Answer: All the information collected for each element in a study.
Rationale: In statistics, an observation is the complete set of data collected for a
single element. For example, if a study collects age, height, and weight for each
person, the set of age, height, and weight for one person constitutes one
observation. This is distinct from a single data point—it encompasses all measured
variables for that element .
b) Element
Correct Answer: In a data set, the individual and unique entry about which data
has been collected, analyzed, and presented in the same manner.
Rationale: An element (also called a "member" or "individual unit") is the
fundamental entity being studied. Each element contributes one observation to
the data set. Elements can include individual people, companies, products, or any
other distinct unit of analysis .
c) Variable
, Correct Answer: A particular, measurable attribute that the researcher believes is
needed to describe the element in their study.
Rationale: Variables are characteristics or properties that can vary among
elements in a study. Examples include age, gender, income, test scores, or blood
pressure. Variables can be either quantitative (numerical) or qualitative
(categorical) .
2. Explain what an outlier is in a data set.
Correct Answer: An outlier is a value that is out of place compared to the other
values in a data set. It may be too large or too small compared to the other
values.
Rationale: Outliers are extreme values that differ significantly from other
observations. They can occur due to measurement error, data entry errors, or
natural variation in the population. Identifying outliers is critically important
because they can heavily influence statistical measures like the mean and can
distort the results of data analysis .
3. Distinguish between descriptive and inferential statistics.
Correct Answer: Descriptive statistics involve analyses that provide a way to
summarize and describe data (e.g., mean, median, mode, standard deviation,
range). Inferential statistics are performed in order for researchers to make
inferences and generalizations about populations based on data gathered from
samples.
Rationale: Descriptive statistics help us understand what the data shows, while
inferential statistics use probability to draw conclusions about a larger population
from a smaller sample. Descriptive statistics describe; inferential statistics predict.
Both branches are essential for comprehensive data analysis .
