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Chapter 1

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McGill University

Mathematics & Statistics (Sci)

MATH 203

Patrick Reynolds

Fall

Description

Math 203: Chapter 1
What is statistics?
-The science of data. It involves collecting, classifying, summarizing, organizing, analyzing, presenting,
and interpreting numerical information.
Descriptive statistics - utilizes numerical and graphical methods to look for patterns in a data set, to
summarize the information revealed in a data set, and to present that information in a convenient form.
Inferential statistics - utilizes sample data to make estimates, decisions, predictions, or other
generalizations about a larger set of data.
Fundamental elements:
a) Experimental unit: an object used to collect data
b) Population: a set of units studied
c) Variable: characteristic property of an individual experimental unit in a population
d) Sample: sub-set of units in a population
Ex: Pepsi wanted to know people’s cola preference. Their sample size was 1000 consumers.
Population: all cola drinkers
Variable: cola preference
Sample: 1000 sampled consumers
Statistical Inference – estimate, prediction, or some other generalization about a population based on
information contained in a sample.
Measure of Reliability – statement (usually quantitative) about the degree of uncertainty associated
with statistical inference.
Ex: If 560 sampled consumers prefer Pepsi, statisticians employed @Pepsi may infer 56% of ALL
cola consumers like Pepsi
4 Elements of Descriptive Statistic Problems:
1) Population/sample of interest
2) Variable(s) investigated
3) Tables, graphs, numerical summary tools
4) Identification of patterns in the data
5 Elements Inferential Statistic Problems:
1) Population/sample of interest
2) Variable(s) investigated
3) Sample of population units
4) Inference about population based on the information contained in the sample
5) Measure of reliability of the inference
Quantitative data – measurements recorded on a naturally occurring numerical scale
Qualitative data – measurements that cannot be measure on a numerical scale; can only be classified
into one of a group of categories **even if you can associate numbers with data, it does not necessarily mean its quantitative**
Designed experiment – a data collection method where the researcher exerts full control over
characteristics of experimental units sampled. Experiments typically involve a group of experi

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