D772 Statistical Data Literacy Notes COMPLETE NEW UPDATE 2025 (you will thank me later Owls)
Western Governors University
Statistical Data Literacy
Populations vs. Samples: Key Differences and Examples
Term Definition Example
The entire group of
All high school
Population individuals or objects
students in the
that you want to
United States.
study.
A smaller, more
A group of 500
manageable group
high school
Sample selected from the
students from
population to
different states
represent the larger
across the U.S.
group.
Numerical values often describe the characteristics of populations
and samples. These values are known as parameters and
statistics.
Understanding the difference between these two terms is essential
for interpreting statistical results and drawing meaningful
conclusions from data.
Parameters:
o A parameter is a numerical value describing an entire
population's characteristics. It is a fixed value, but it is
often unknown because collecting data from every
member of a large population is usually impractical or
, impossible.
Statistics:
o A statistic is a numerical value that describes a
characteristic of a sample. It is calculated from the data
collected from the sample and used to estimate the
corresponding population parameter. Since we cannot
measure the entire population, statistics are essential
for making inferences and generalizations about the
broader group.
Parameters vs. Statistics Examples
, Term Definition Example
A numerical value
The average
that describes a
Parameter height of all adult
characteristic of a
women in the
population.
United States.
A numerical value The average height of
that describes a 100 adult women
Statistic
characteristic of a randomly selected
sample. from the United
States.
In the context of data collection, it is important to understand the
basic elements that make up a dataset: individuals, variables, and
data. These elements are the building blocks of any statistical
analysis, and a clear understanding of them is crucial for
interpreting and drawing conclusions from data.
Individuals are the objects described by a set of data. These can
be people, animals, or things. In essence, they are the entities on
which we collect information.
Variables are the characteristics or measurements that we are
interested in studying. They are the specific aspects of the
individuals that we collect data on. Variables can be either
quantitative (numerical) or categorical (qualitative).
•
o Quantitative variables: These are numerical
measurements, such as age, height, weight, or
income.
o Categorical variables: These are categories or
labels, such as gender, race, occupation, or favorite
color.
Data are the actual values of the variables. Although the word is
not used very often, the word "datum" is the singular form of the
plural data. Data are the raw information that we collect and
analyze to gain insights into the phenomenon we are studying.
, One of the most reliable and unbiased sampling methods is simple
random sampling. In a simple random sample, all individuals are
put into a single list, and we randomly select from that list until we
reach the desired sample size. While almost all sampling methods
involve some type of randomness, with a simple random sample,
the emphasis is on the word "simple." We do not impose any
additional structure or process for selection. All the names go into
the same metaphorical hat, then we randomly select a certain
number of them.
This gives us the important property that for a particular sample
size, n, any combination of n individuals is equally likely to be
selected. This also helps ensure that the sample is not skewed
towards any particular group or characteristic within the
population, making the data collected more trustworthy.
Stratified sampling involves dividing the population into distinct
subgroups called strata, based on specific characteristics such as
age, gender, or socioeconomic status. Once the population is
divided into strata, a random sample is taken from each stratum in
proportion to its representation in the overall population. This
ensures that the sample reflects the diversity of the population in
terms of the chosen characteristics.
Cluster sampling involves dividing the population into clusters,
which are naturally occurring groups like schools, neighborhoods,
or cities. Instead of randomly selecting individuals from the entire
population, researchers randomly select a few clusters and
include all individuals within those selected clusters in the sample.
This method is often used when it's difficult or expensive to
sample individuals directly from the entire population.
Systematic sampling involves selecting every "nth" individual
from a list of the population, starting from a randomly chosen
point. This method is often used when it's easy to access a list of
the entire population. It's a simple and efficient method.
Observational Studies:
• In an observational study, researchers observe and
record data on variables as they naturally occur, without
any intervention or manipulation.
• Example: A researcher observes and records the eating
habits and weight of a group of individuals over a year to
see if there is a relationship between diet and weight
Western Governors University
Statistical Data Literacy
Populations vs. Samples: Key Differences and Examples
Term Definition Example
The entire group of
All high school
Population individuals or objects
students in the
that you want to
United States.
study.
A smaller, more
A group of 500
manageable group
high school
Sample selected from the
students from
population to
different states
represent the larger
across the U.S.
group.
Numerical values often describe the characteristics of populations
and samples. These values are known as parameters and
statistics.
Understanding the difference between these two terms is essential
for interpreting statistical results and drawing meaningful
conclusions from data.
Parameters:
o A parameter is a numerical value describing an entire
population's characteristics. It is a fixed value, but it is
often unknown because collecting data from every
member of a large population is usually impractical or
, impossible.
Statistics:
o A statistic is a numerical value that describes a
characteristic of a sample. It is calculated from the data
collected from the sample and used to estimate the
corresponding population parameter. Since we cannot
measure the entire population, statistics are essential
for making inferences and generalizations about the
broader group.
Parameters vs. Statistics Examples
, Term Definition Example
A numerical value
The average
that describes a
Parameter height of all adult
characteristic of a
women in the
population.
United States.
A numerical value The average height of
that describes a 100 adult women
Statistic
characteristic of a randomly selected
sample. from the United
States.
In the context of data collection, it is important to understand the
basic elements that make up a dataset: individuals, variables, and
data. These elements are the building blocks of any statistical
analysis, and a clear understanding of them is crucial for
interpreting and drawing conclusions from data.
Individuals are the objects described by a set of data. These can
be people, animals, or things. In essence, they are the entities on
which we collect information.
Variables are the characteristics or measurements that we are
interested in studying. They are the specific aspects of the
individuals that we collect data on. Variables can be either
quantitative (numerical) or categorical (qualitative).
•
o Quantitative variables: These are numerical
measurements, such as age, height, weight, or
income.
o Categorical variables: These are categories or
labels, such as gender, race, occupation, or favorite
color.
Data are the actual values of the variables. Although the word is
not used very often, the word "datum" is the singular form of the
plural data. Data are the raw information that we collect and
analyze to gain insights into the phenomenon we are studying.
, One of the most reliable and unbiased sampling methods is simple
random sampling. In a simple random sample, all individuals are
put into a single list, and we randomly select from that list until we
reach the desired sample size. While almost all sampling methods
involve some type of randomness, with a simple random sample,
the emphasis is on the word "simple." We do not impose any
additional structure or process for selection. All the names go into
the same metaphorical hat, then we randomly select a certain
number of them.
This gives us the important property that for a particular sample
size, n, any combination of n individuals is equally likely to be
selected. This also helps ensure that the sample is not skewed
towards any particular group or characteristic within the
population, making the data collected more trustworthy.
Stratified sampling involves dividing the population into distinct
subgroups called strata, based on specific characteristics such as
age, gender, or socioeconomic status. Once the population is
divided into strata, a random sample is taken from each stratum in
proportion to its representation in the overall population. This
ensures that the sample reflects the diversity of the population in
terms of the chosen characteristics.
Cluster sampling involves dividing the population into clusters,
which are naturally occurring groups like schools, neighborhoods,
or cities. Instead of randomly selecting individuals from the entire
population, researchers randomly select a few clusters and
include all individuals within those selected clusters in the sample.
This method is often used when it's difficult or expensive to
sample individuals directly from the entire population.
Systematic sampling involves selecting every "nth" individual
from a list of the population, starting from a randomly chosen
point. This method is often used when it's easy to access a list of
the entire population. It's a simple and efficient method.
Observational Studies:
• In an observational study, researchers observe and
record data on variables as they naturally occur, without
any intervention or manipulation.
• Example: A researcher observes and records the eating
habits and weight of a group of individuals over a year to
see if there is a relationship between diet and weight
