Chapter 1

Introduction to the statistics

Chapter One

What is Statistics?What is Statistics?

ONEUnderstand why we study statistics.TWOExplain what is meant by descriptive statistics and inferential statistics.THREEDistinguish between a qualitative variable and a quantitative variable.FOUR Distinguish between a discrete variable and a continuous variable.FIVEDistinguish among the nominal, ordinal, interval, and ratio levels of measurement.SIXDefine the terms mutually exclusive and exhaustive.

GOALSWhen you have completed this chapter, you will be able to:

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History of statistics

• The history of statistics can be said to start around 1749 although, over time, there have been changes to the interpretation of what the word statistics means. In early times, the meaning was restricted to information about states. This was later extended to include all collections of information of all types, and later still it was extended to include the analysis and interpretation of such data. In modern terms, "statistics" means both sets of collected information, as in national accounts and temperature records, and analytical work which requires statistical inference.

History of statistics

• Statistical activities are often associated with models expressed using probabilities, and require probability theory for them to be put on a firm theoretical basis: see History of probability.

• A number of statistical concepts have had an important impact on a wide range of sciences. These include the design of experiments and approaches to statistical inference such as Bayesian inference, each of which can be considered to have their own sequence in the development of the ideas underlying modern statistics.

• Contents

Why study statistics?

• Numerical info is everywhere– But how do we know if conclusions reported are

accurate?

• Statistical techniques are used to make decisions that affect our lives– This is why younger people pay more for insurance…

• Knowledge of statistical methods at least helps you understand why decisions are made – In future you will make decisions that involve data

What is Meant by Statistics?

• Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data to assist in making more effective decisions.

In common usage statistics refers to numerical information….. But in this course the term has a wider meaning….

Who Uses Statistics?

• Statistical techniques are used extensively by managers in marketing, accounting, quality control, consumers, professional sports people, hospital administrators, educators, politicians, physicians, gamblers, etc...

Types of Statistics

• Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.

EXAMPLE 1: A Gallup poll found that 49% of the people in a survey knew the name of the first book of the Bible. The statistic 49 describes the number out of every 100 persons who knew the answer.

Types of Statistics

• Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.

EXAMPLE 2: According to Consumer Reports, General Electric washing machine owners reported 9 problems per 100 machines during 2002. The statistic 9 describes the number of problems out of every 100 machines.

Types of Statistics

• Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.

EXAMPLE 3: The Canadian government reports that the population of Canada was 18,238,000 in 1961, 21,568,000 in 1971, 24,820,000 in 1981, 28,031,000 in 1991, and 31,050,700 in 2001. If we calculate percentage growth over the decades it is also descriptive statistics.

Types of Statistics • Inferential Statistics: The methods

used to determine something about a population, based on a sample.

O EXAMPLE 1: In the preceding example on Canadian population changes, if you use the past data to forecast the population of Canada in the year 2010 or expected percentage of growth from 2000 to 2010, then this is considered inferential statistics.

Types of Statistics • Inferential Statistics: The methods

used to determine something about a population, based on a sample.

EXAMPLE 2: The accounting department of a large firm will select a sample of the invoices to check for accuracy for all the invoices of the company.

Types of Statistics • Inferential Statistics: The methods

used to determine something about a population, based on a sample.

EXAMPLE 3: Wine tasters sip a few drops of wine to make a decision with respect to all the wine waiting to be released for sale.

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Population vs. Sample

Population is the entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest.

Sample is a portion, or part, of the population of interest

See also p.7

Population: All items

Sample: Items selected from the population

• NB: don’t confuse population in statistics with a country’s population!

• A population might consist of all the people in Nanaimo but also may mean the PE ratios for all chemical stocks, or total assets of the 20 largest banks in North America, total collection of prices, ages, square footage of retail space in Nanaimo, and so on.

Types of Variables

• For a Qualitative or Attribute variable the characteristic being studied is nonnumeric.

EXAMPLES: Gender, religious affiliation, type of automobile owned, country of birth, eye colour are examples.

Types of Variables

•

• In a Quantitative variable information is reported numerically.

EXAMPLES: balance in your chequing account, minutes remaining in class, or number of children in a family.

Types of Variables

• Quantitative variables can be classified as either discrete or continuous.

••Discrete variables: can only assume certain values and there are usually “gaps” between values.

EXAMPLE: the number of bedrooms in a house, or the number of hammers sold at the local Home Depot (1,2,3,…,etc). But you cannot have 2.3 bedrooms or 10.6 hammers…Thus discrete variables result from counting.

Types of Variables

• A continuous variable can assume any value within a specified range.

• Examples are: The pressure in a tire, the weight of a pork chop, or the height of students in a class. Typically, continuous variables are the result of measuring something.

Summary of Types of Variables

Q u a lita t ive o r a ttrib u te(typ e o f ca r ow n ed )

d isc re te(n u m b er o f ch ild ren )

con tin u ou s(t im e taken fo r an exam )

Q u an tita tive o r n u m erica l

D A TA

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