Chapter 1: Introduction to Business Statistics
Population and Samples
Population: A set of units (usually people, objects, or events)
o Ex. All of last year’s graduates from an MBA program
Variable: A measureable characteristic of a population unit
o Quantitative: Variables that are numbers or quantities
Usually consists of ‘how much’ or ‘how many’
Ex. Starting salary of last year’s graduates of an MBA program
o Qualitative: Variables that are categorical to which a population unit belongs
Ex. A person’s sex.
Measurement: Process of determining the quantity or extent of the variable for some particular unit of the population.
o Ex. Measuring the starting salary of an MBA graduate to the nearest dollar
Value: The specific measurement for a particular unit in the population (result of measurement)
o Ex. Starting salary of an MBA graduate to the nearest dollar
Population of measurement (observation): Measurement of the variable of interest for each and every population unit
o Census: An examination of the entire population of measurement
o Ex. Annual starting salaries of all graduates from last year’s MBA program
Sample: A selected subset of the population
o Often, the population is too large, and it is too expensive and time-consuming to conduct a census.
o Ex. A selected subset of last year’s MBA graduates
Sample of measurement: Measurement of the variable of interest of the sample.
o Ex. Annual starting salaries of selected graduates from last year’s MBA program
Descriptive statistics: The science of describing the important aspects of a set of measurements
o If the population is small, a census of the population can be obtained.
o If the population is large, a sample needs to be selected, and statistical inference is required.
o Ex. For a set of starting salaries of last year’s MBA graduates, wishing to know much is the average
Statistical inference: The science of using a sample of measurements to make generalizations about the important
aspects about a population of measurement
o Estimating the important aspects of a population of interest.
o Ex. Use a sample of starting salaries to estimate the average of population of starting salaries.
Sampling a Population of Existing Units
Random sample: A sample selected so that each population has the same chance of being selected as every other unit.
Random number table: Computerized methods of selecting a random sample, in case of enormous population
Selecting a random sample:
o Sample with replacement: Replace every sampled unit before picking the next unit
Every unit remains as candidates for every selection.
For some instances, the sample does not contribute new information. o Sample without replacement: Do not replace every sampled unit before picking the next unit
Every unit that has already been selected is not given a chance to be re-selected.
Recommended for most instances, since this gives us the fullest possible look at the population.
Approximately random samples:
o Frame: A list that identifies every individual population unit.
For small populations, frames can be created to create a random sample.
o Systematic sample: Randomly enter the population and systematically sample each k unit.
If the population is large, it is not possible to list every individual population unit.
Ex. intercepting every 100 customer at the mall, and requesting for participation in the survey.
o Voluntary response sample: Participants select themselves to be in the survey
Non-scientific, because it is not representative of the population.
Large amount of the sample consists of individuals with strongly sided opinions
Sampling a Process
Process: A sequence of operations that take input (labour, material, methods, machine, etc.) and them into outputs
(products, services, etc.)
Population: All output produced in the past, present, and future.
o Finite population: Population that is fixed, limited in size, and countable
Ex. Every Toyota Corolla that was produced last year.
o Infinite population: Population that is unlimited or counting is impossible.
Sampled at equally spaced time points.
Ex. Every Toyota Corolla that will be produced next year.
Statistical control: A process is in statistical control if it does not exhibit any unusual process variations.
o Runs-plot (time-series plot): A graph of individual process measurement versus time.
o The process usually displays a constant amount of variation, around a constant or horizontal level.
o The process is predictable, and allows the researcher to make statistical inferences about the population.
o To determine if a process is in control, sample the process often enough to detect unusual var