Topic:Introduction to Business Statistics
From SharedExperienceProject
Contents |
Topic Highlights
(What you will learn)
- A first look at why it's important for businesspeople to learn statistics
- How the term statistics is defined
- Insight into the decision-making process and the two types of statistics (descriptive and inferential) that are involved
- The concepts of populations and samples, and parameters and statistics
Introduction and Motivation
(Why learn it)
To set the stage and provide an understanding of why one would study statistics, this topic is often used early on in a course on business statistics. It is important because:
- We will look at why statistics is important to learn
- We will get a feel for what it's going to be like to learn it together this term.
Learning Activities
(What I need to do to meet the objectives given below)
| Type | Name | Direction |
| Reading |
| Self-directed |
| In-class worksheet | Self-directed | |
| In-class discussion |
| Instructor-directed |
| Personal activities |
| Self-directed |
Learning Objectives
(Levels of understanding to be gained)
| Level of Understanding | Objective(s) (presented as self-assessment questions) |
| Very best |
|
| Highly satisfactory |
|
| Satisfactory |
|
| Maybe just enough to pass |
|
Topic Notes: Statistics - What and Why?
These lecture notes are intended to facilitate an introductory discussion on the topic of statistics.
What is Statistics?
Definitions alone don't often tell us much, but they do provide a good starting point:
- Statistics is the science comprising rules and procedures for collecting, describing, analyzing and interpreting numerical data[2].
In the following, let's try to figure out what this means.
Why is Statistics Important in Business?
Simply put, statistics is important because we use it for planning and to make decisions. Whether we realize it or not, we do this every day as individuals and as stakeholders of companies.
A generic business decision-making process is given in the figure below. You should observe the two main elements, which are shown by the yellow boxes:
1. The use of an appropriate statistical model for describing data that you have collected (about variables of interest to you or your company)
2. The analysis of that description to help you make the best possible decision
| The statistical decision-making process |
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These two parts of the process give rise to the distinction between two kinds of statistics:
1. Descriptive statistics:
- The process of representing the the real world with an appropriate statistical model
- It is here that we collect data, make assumptions and describe variables of interest in quantitative ways (both numerical and graphical)
2. Inferential statistics:
- The process of analyzing and interpreting the quantitative description, in order to address the real world problem
- It is here that we can draw conclusions and make decisions for a positive outcome
Example 1
Would you describe each of the following as an example of descriptive or inferential statistics?
a) A student learns about the findings of a study by reading a newspaper article with the headline "Heavy drinkers more likely to injure themselves", and decides to change his partying behavior
b) A production manager measures the rate of failure of parts being assembled under his supervision, and creates a histogram based on the data
c) A manager pays a marketing consultant to collect data about her company's customer base
d) The CEO of a start-up forecasts the company's profits based on data in previous financial statements and based on market data obtained from the company's marketing guy
e) A product manager analyzes key economic indicators, demographic trends and the size of a several market segments to forecast sales for next year
f) An employee in Human Resources is asked to analyze the hiring data for the previous seven years and to generate a report for the HR Manager
g) The HR Manager analyzes the report, notices that the R&D Manager never hires short people, and decides to speak to that manager about it
Example 2
Can you think of other examples where statistics would help you make a decision in business? In your personal life?
Topic Notes: Populations, Samples, Parameters and Statistics
These notes are intended to facilitate a discussion on the topic of populations and samples.
Population vs. Sample
In an earlier topic (Variables in Data Sets), we discussed the concept of variables of interest to a manager. In the discussion above (Statistics - What and Why?), we took the concept a little further by describing the process through which that manager uses statistics to reach a decision. Throughout both of those discussions, we simply assumed that we had (or could get) the data we needed to learn about the variable of interest. Things are a little more complex than that in reality, however, because of the difference between a population and a sample. The business student needs to understand this.
The example and figure below provide a useful explanation.
Example 3
Imagine that you are responsible for designing a promotional plan for a fancy new kind of running shoe, for a segment of the Canadian population (represented in the figure below as the "target population.") You are interested in two parameters:
- Ideally, you want to know the average amount each person in the entire population is willing to spend on a new pair of shoes (i.e. the mean price)
- Because your company's shoe designers are having a hard time getting it right, you are also interested in how much variation in price potential customers will put up with (i.e. the standard deviation of the prices)
Because there are millions of people in your target population, it would cost your company millions of dollars to survey all of them - not going to happen. Instead, you can probably only afford to send a survey out to a subset of the total population (say, 1000 people, represented below as the "sample frame").
This is what will happen:
- Some people will not respond (or will provide bogus answers), represented below as the "non-responders"
- There will be others who respond, but who are not even part of your target population, represented as "ineligible"
- You will be left with the shaded group below, known as the sampled population, or sample
- From the data in this sample, you can obtain sample statistics:
- The sample mean, which provides insight into the mean of the population
- The sample standard deviation, which provides insight into the standard deviation of the population
| The difference between a population and a sample |
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Parameter vs. Statistics
From the above example, you should already understand the difference between a parameter and a sample. Just in case, let's review:
- A population is the set of all possible measurements, usually pertaining to the variable of interest
- Parameters define the characteristics of the entire population
- A sample is a subset of the population, selected to represent the population
- Statistics, which are obtained by analyzing the data collected from the sample, define the characterstics of the sample
- The idea is that a statistic provides insight into the corresponding parameter of interest
Some parameters and their corresponding statistics are shown in the figure below, along with the symbols usually used in statistics for representing them.
| Parameters and statistics |
|---|
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The Importance of Sample Size
It should make sense to you that a sample statistic will better represent the parameter of interest if:
- You collect more data, i.e. use a larger sample
- You make sure your sample is a random sample
Finally, it is worth noting that a sample taken of a whole population is known as a census. This provides the best possible representation of the parameters of interest, but it only happens when the population is very small, or the resources are very large.
Practice Problems
Practice Problem 1
In the following figure:
a) Can you identify the population and the sample, and explain the difference between them?
b) From which would the sample mean be calculated?
Practice Problem 2
Can you answer the questions posed above under the heading Learning Objectives?
Footnotes
- ↑ Explaining to your friends why statistics is important is harder than explaining it to your parents; your explanation has to be solid because statistics is just not that cool a topic of conversation.
- ↑ Kvanli, A.H., R.J. Pavur and K.B. Keeling (2003) Introduction to Business Statistics, Thomson Nelson, 917 p.
