Statistics Chapter 1: Sampling and Data

Sampling and Data- week 1: September 9th, 2026

What is a population?

The entire group of individuals, objects, or measurements whose properties are being studied.

What is a sample?

A subset of the population.

Why do we use a sample instead of studying the entire population?

• too time-consuming

• expensive

• impractical

What is a representative sample?

A sample that has approximately the same characteristics as the population.

What is a statistic?

A numerical characteristic of a sample.

What is a parameter?

• A numerical characteristic of the entire population.

• Calculated the average GPA of every student in the population:

  Their average GPA = parameter

• Parameter → Population

  
  
  

What is the relationship between a statistic and a parameter?

A statistic is used to estimate a population parameter.

Which describes a sample: statistic or parameter?

Statistic.

Which describes a population: statistic or parameter?

Parameter.

What is qualitative data?

Data consisting of labels or names rather than numerical measurements.

What is quantitative data?

• Data consisting of numerical values.

• Age, height, income, or number of children.

What is discrete data?

• Quantitative data that can be counted and usually take separate, distinct values.

• Ex: Number of students in a class.

What is continuous data?

• Quantitative data that can be measured and can take any value within a range.

• Ex: A person's height or weight.

What is random sampling?

A sampling method in which each member of the population has an equal chance of being selected.

What is a simple random sample?

Number each population member and use a random method to select the sample.

What is stratified sampling?

1. Divide the population into groups called strata.

2. Take a proportion from each group.

3. Use random sampling within each group.

What is cluster sampling?

1. Divide the population into clusters

2. randomly select some entier clusters

3. Include all members of the selected clusters.

What is systematic sampling?

Start at a random point and select every K^th individual.

What is convenience sampling?

A nonrandom method that selects individuals who are easily accessible.

What is the main problem with convenience sampling?

It can produce a biased sample because not everyone has an equal chance of being selected.

What is sampling error?

Errors caused by the sampling process itself.

Example:

• The sample isn't large enough.

What happens to sampling error as sample size increases?

Sampling error generally decreases.

What is nonsampling error?

Errors caused by factors not related to the sampling process.

Examples:

• Defective counting device

• Data-entry errors

• Flawed/poorly worded survey questions

• Nonresponse/refusal

What is sampling bias?

Some members of the population are more likely to be selected than others.

Why can a large sample still be biased?

A large sample does not fix a biased method of selecting participants.

What is frequency?

The number of times a particular value occurs.

What is relative frequency?

The ratio of a value's frequency to the total number of observations.

What is cumulative relative frequency?

Total of the relative frequencies up to a particular value.

What is a proportion/How do you calculate it?

Proportion = number of successes ÷ total number of observations.

What does "at most" mean?

Less than or equal to.

What does "at least" mean?

Greater than or equal to.

If a question asks for the proportion of people with a value "at most 10," what values are included?

All values less than or equal to 10.

What is variation in data?

The fact that individual observations can differ from one another.

Why can data vary?

Different:

• individuals

• measurements

• amounts

• methods

• accuracy

What is variation in samples?

The fact that two different random samples from the same population can produce different results.

Why can two random samples give different results?

Random sampling produces natural variation from sample to sample.

What are the four levels of measurement?

Nominal, ordinal, interval, and ratio.

What is nominal measurement?

• Categories or labels with no meaningful order.

• Ex: Eye colour or type of car.

What is ordinal measurement?

• Categories that CAN be ordered/ranked.

• But the differences between rankings cannot be measured.

• Ex: Class ranking or satisfaction level.

What is interval measurement?

• Numerical data with meaningful differences between values

• no true zero

• Ex: Temperature measured in Celsius.

What is ratio measurement?

• Numerical data with meaningful differences and a true zero.

• Ex: Height, weight, or income.

What is the rounding rule for statistical calculations?

The final answer should generally have one more decimal place than the original data.

What are descriptive statistics?

Methods used to organize and summarize data using graphs, numbers, or other summaries.

What are inferential statistics?

Methods used to draw conclusions about a population from sample data, using probability.

What is an explanatory variable?

• The variable researchers control or manipulate that might cause or explain a change in another variable.

• Example: Type of fertilizer → might cause a change in plant growth.

What is a response variable?

• Variable being measured to determine whether it changes in response to the explanatory variable.

• Example: Whether or not a person has a heart attack when testing aspirin.

What are treatments?

• The different values of the explanatory variable

• Ex: Aspirin vs. placebo

What is an experimental unit?

The individual or object being measured in an experiment.

What is random assignment?

Researchers randomly assign experimental units to different treatment groups.

Why is random assignment important?

• Spread lurking variables among the treatment groups

• allows researchers to better determine cause-and-effect

What is a lurking variable?

• An additional variable that can interfere with the relationship being studied.

• Ex: Researchers notice that people who regularly take vitamin E have better health.

Does that prove vitamin E causes better health?

No.

People who take vitamin E may also:

• Exercise

• Eat healthier

• Take other supplements

• Not smoke

What is a control group?

• Group in a randomized experiment that receives an inactive treatment

• is otherwise managed in the same way as the treatment group

What is a placebo?

• Inactive treatment that cannot directly affect the response

• used to account for the power of suggestion

What is blinding?

Not telling participants which treatment they are receiving.

What is double-blinding?

Both the participants and the researchers who work with them do not know which treatment the participants are receiving.

What is causality?

• One variable causes a change in another variable

What is confounding?

• Effects of multiple factors cannot be separated

• difficult to determine which variable is actually causing the observed result

• Ex: Studying more is related to higher grades, but sleep or tutoring could also affect grades, so we can't tell if studying itself caused the higher grades.

What does N represent in sampling formulas?

The population size — the total number of individuals in the population.

What does n represent in sampling formulas?

The sample size — the number of individuals in the sample.

What is the formula for k in systematic sampling?

k = N ÷ n

What does k represent in systematic sampling?

• The sampling interval — how many individuals you skip/select between selections.

• Ex: every 5th person

What are the five main sampling methods?

1. Simple random sampling

2. Stratified sampling

3. Cluster sampling

4. Systematic sampling

5. Convenience sampling

What is the difference between N and n?

N = population size; n = sample size.

What is the formula for relative frequency?

• RF = f ÷ n

• f = frequency

• n = total number of observations

How do you find the total number of observations when you know frequency and relative frequency?

n = f ÷ RF