Foundations of
Business Statistics
COMM 104 Module 1 Lecture
Outline for today
- Course syllabus highlights
- Introduction to statistics: populations, samples, parameters, and statistics
- Sampling methods
- Simple random sampling (with and without replacement)
- Stratified random sampling
- Cluster random sampling
- Voluntary response sampling
Course syllabus highlights
- 11 course modules
- 3 assignments, best 2 of 3, 5% each (total: 10%)
- 10 module quizzes, 0.5% each (total: 5%)
- Bonus Quiz replaces your worst module quiz grade
- 1 midterm, 40%
- Final exam, 45% (must pass average of the two in-person assessments
to pass the course)
- Course text is free, available on Canvas
- Please ensure you have Microsoft Excel and a scientific calculator
(graphing calculators not permitted)
Course syllabus highlights: Integrity
Academic integrity:
-
You may discuss any take-home assessment with others
-
You may tell someone else where you found a question similar to one on an
assignment, but you may not share your answer
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You may not post any course material to any external sites
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You may use Microsoft Copilot to help generate ideas, or get you started, etc.
However, you will likely get a very bad grade on the in-person assessments (i.e.,
the midterm and the final exam) if you do so.
Course syllabus highlights: Help
- Carolyn’s office hours: Wednesdays 9:00 - 11:00 AM, Zoom
- The Math & Stats Help Centre in Murray Library
- Modules have a set of optional extra help videos from a different
instructor, so you can see the material from a different perspective.
- Private tutors
Introduction to business statistics
Statistics is the study of estimation and inference
- Estimation: how well can we guess a particular quantity?
- Inference: based on our estimated quantity, what kind of
decisions can we make and how confident can we be in
those decisions?
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Why do I need statistics in business?
Indeed.com, which claims to be the #1 job site in the world, says
business professionals need statistics to:
1.
2.
3.
4.
5.
6.
Gather reliable data (COMM 104 Module 1)
Understand probability (COMM 104 Module 4)
Make inferences (COMM 104 Module 11 and COMM 207)
Plan changes (COMM 104, 205, 207, 393, 395, etc.)
Predict cause and effect (COMM 207 a little, more in other courses)
Develop analytical skills (COMM 104, 121, 207, etc.)
Source: https://www.indeed.com/career-advice/career-development/statistic-benefits
Why do I need statistics in business?
Indeed.com, which claims to be the #1 job site in the world, says
business professionals need statistics to:
7. Learn surveying skills (COMM 357 especially)
8. Use averages (COMM 104 Modules 1, 2, 9; COMM 207, 205, etc.)
9. Recognize false claims (COMM 104 Module 11 and COMM 207)
10. Identify variables (COMM 104 Module 3, etc.)
11. Recognize correlations (COMM 207 Modules 5, 6, 7)
12. Track changes (COMM 395, etc.)
13. Communicate data (COMM 104, 207, etc.)
Source: https://www.indeed.com/career-advice/career-development/statistic-benefits
Example 1
Suppose you are the quality assurance specialist for a major company that sells
canned dog food. The company claims that each can contains 130g of dog food.
Part of your job is to evaluate that claim.
You obtain 100 cans and find that the average (mean) weight of the food is 140g.
Is this value different enough from the claim that you would consider the claim to
be incorrect?
We will revisit this later in the course when we discuss hypothesis testing. If you
conclude that the claim is incorrect, you may recommend changes to the
production process. This is an example of a business decision that statistics can
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help you make.
Introduction to business statistics
We will now define some key terms to be used in the course, based on the
example
Unit, individual, element, case: an object or person on which measurements are
taken (e.g. a single can of dog food)
Population: the set of all units of interest (e.g. all cans of dog food that could ever
be created by this manufacturing process at this facility)
- A population can be finite or infinite
- In the example, we had an infinite population
- A finite population could be, for example, the set of all Canadian citizens on
Jan 7th 2026 at 8:50 AM.
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Introduction to business statistics
Sample: a set of units chosen in some way from a population (e.g. 100 cans of
dog food)
Sample size: the number of units in the sample, often denoted n (e.g. n=100)
Population size: the number of units in the population, often denoted N
(e.g. N = infinity)
Statistic: a characteristic of a sample (e.g. sample mean weight = 140 g)
Parameter: a characteristic of a population (e.g. population mean weight of all
cans of dog food)
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Introduction to business statistics
- Populations and parameters
- Samples and statistics
- Calculating your first statistic and understanding what it means
- Calculating your first parameter and understanding what it means
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Example 2
Suppose we are interested in estimating the average waiting time for a
call to be answered in a help centre for an IT company. Since the calls are
recorded, we have the waiting time for the last three callers: 10 minutes,
3 minutes, and 8 minutes, respectively.
a)
b)
c)
d)
What is the sample size?
Do we know the population size? Is the population finite, or infinite?
Calculate the sample mean
What is an example of a business decision that could be made
based on the sample mean? What other information do we need
before a decision can be made?
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Example 3
Suppose you have a garden bed of 5 zucchini plants. You keep track of the
number of zucchinis produced by each plant, given below (i.e. you have a census:
you have measured every single element in the population).
Plant number
1
2
3
4
5
# zucchini
8
9
10
5
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a) Calculate the population mean.
b) Suppose you only have data for plants 1, 2, and 3. That is, you have a sample
of number of zucchinis produced by the first three zucchini plants. Calculate
the sample mean.
c) Do you think your answer to part (b) is a good estimate of the population
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mean? Why or why not?
Sampling and sampling bias
Recall a sample is a subset of a population
We want a representative sample
We saw an example of sampling bias: an effect in which some units in the
population have a higher chance of being selected in the sample than others.
- E.g. “The first three zucchini plants” - this was a convenience sample: the
first three were probably close to the beginning of the row of vegetables,
so we selected them because they were conveniently located. They
happened to have a higher yield than the other two plants.
Simple random sampling
In a simple random sample, each unit in the population has an equal
chance (probability) of being selected, and that probability is 1/N.
Example: Suppose it’s 2021, and you’re interested in obtaining a
sample of Canadians. In 2021, Statistics Canada reported the
population of Canada was 36,991,981 at the time of the census. In a
simple random sample, each Canadian would have a probability of
approximately 1 in 37 million of being selected.
Source: Statistics Canada. Canada, provinces and territories. https://www12.statcan.gc.ca/census-recensement/index-eng.cfm
Simple random sampling without
replacement
A simple random sample in which each population unit may only
be chosen once
Simple random sampling with
replacement
A simple random sample in which each population unit may be chosen
more than once
Population: 1, 2, 3, 4, 5, 6, 7, 8, 9
Sample: 1, 1, 5, 6
Each unit had probability 1/9 of being selected
The unit ‘1’ happened to be chosen twice
Example 4
For each of the following situations, determine if sampling is being
conducted with or without replacement. Is this a simple random
sample? Name a source of bias for each of these samples.
a) A produce manager at a grocery store selects 5 tomatoes from
the top of each delivered crate to determine freshness.
Example 4
For each of the following situations, determine if sampling is being
conducted with or without replacement. Is this a simple random
sample? Name a source of bias for each of these samples.
b) An auditor selects a sample of 100 transactions for a company
they’re auditing; the 10 highest transactions are included in the
sample.
Example 4
For each of the following situations, determine if sampling is being
conducted with or without replacement. Is this a simple random
sample? Name a source of bias for each of these samples.
c) You buy a ticket in a lottery. To win, the 5 numbers on your ticket
must match the 5 numbers announced. The lottery selects the
winning ticket by selecting a number from 1 to 9, written on a
piece of paper, from a hat, putting it back, and repeating the
process until 5 numbers have been announced.
Stratified random sampling
Divide the population into groups (‘strata’) and conduct a simple
random sample within each stratum.
Makes the most sense when the population is easily divided into
groups based on some common characteristic.
Stratified random sampling
Example 5: Say you want to estimate the population mean height
of Canadians. To avoid bias, you select 10 people from each
province and each territory in your sample. Each Saskatchewanian,
for example, would have a 10/1,231,000 chance of being selected
(roughly).
In this example, what are the strata?
Cluster random sampling
Very similar to stratified random sampling. Use the term “cluster”
instead of “stratum”.
Each cluster has an equal probability of being selected.
A census is conducted in each selected cluster (i.e. every unit in the
chosen clusters is measured).
Cluster random sampling
Example 6: Suppose we are interested in comparing performance
in COMM 104 for students from different locations. Suppose
further that students come from Saskatoon (A), Regina (B), Prince
Albert (C), Saskatchewan in general but outside these cities (D),
and outside Saskatchewan (E). We select three locations: A, C, E.
We keep track of all students from each chosen location and
obtain their final grades.
a) In this example, what are the clusters?
b) How do you know this is NOT a stratified random sample?
Voluntary response sampling
In a voluntary response sample, each unit chooses whether to be
selected.
This type of sampling is fraught with bias and should be avoided if
possible.
Voluntary response sampling
Example 7: Drug trials often experience this issue, because
experimental medication is often used as a last resort for patients
who are extremely sick. Because the entire sample consists of
extremely sick patients, there is no way to know whether the drug
would work if the condition had been treated at an earlier stage of
the disease.
Example 8
Identify the type of sampling being used in each of the following
scenarios:
a) A national public health professional in Ottawa is interested in
obtaining a sample of vaccination rates in northern
Saskatchewan communities. They select a sample of 10
communities. The public health professional calls the
community registrar and obtains the total number of
vaccinations in each community.
Example 8
Identify the type of sampling being used in each of the following
scenarios:
b) A school nutritionist is interested in knowing the eating habits of
the eight-year-old children at their school. There are a total of 110
eight-year-old children, and the nutritionist uses a computer
program to select 30 children at random. A parent or guardian of
these 30 students is required to fill out a questionnaire.
To do list
- Go to Modules > Start Here. Proceed from top to bottom to view
all of the videos.
- Go to Modules > Module 1. Proceed from top to bottom to
complete the module.
- Don’t forget to do the Bonus Quiz before Module Quiz 1. You can
find the bonus quiz under Modules > Module 1 > Bonus Quiz
- Recall: Module Quiz 1 is due Jan 18th at 11:59 PM (and you now
have everything you need to complete the quiz)
Summary
- Statistics are characteristics of samples; parameters are characteristics of
populations
- Parameters are often unknown, because we would have to observe every
single unit in the population and that’s usually very expensive. We make do
with a statistic that estimates the unknown parameter.
- A common statistic is the sample mean:
- A common parameter is the population mean:
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Summary
- Simple random sample (SRS): each population unit has an equal chance of
being selected
-
With replacement: each population unit could be chosen more than once for the sample
- Without replacement: each population unit could be chosen a max of once for the sample
- Stratified random sample: divide population to strata; SRS in each stratum
- Cluster random sample: divide population into clusters; a census is conducted
in each chosen cluster
- Voluntary response sample: each population unit chooses whether to be
included in the sample