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Midterm

Department

StatisticsCourse Code

STAB22H3Professor

Mahinda SamarakoonStudy Guide

MidtermThis

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Ch.1 Introduction to Statistics:

What is Statistics?

•A way of reasoning

•A collection of tools and methods to help us understand the world

•All about variation

Who, What, Where, When, Why and How

•Who: individual cases, objects that are described by a set of data

oE.g. people, animals, things

•What: the variables

oCategorical variables – characteristics, can’t be measured or

counted

E.g. hair color, eye color, area code, zip code

oQuantitative variables - #s, units, can be measured or

counted)

E.g. age

•Where: the place in which the variables take place

•When: the time in which the variables take place

•Why: the purpose of the data

Ordinal Scales/Variables:

•Falls between nominal and interval scales

•Have natural ordering of values but undefined interval distances

between the values

oE.g. Social class: upper class, middle class, lower class

Nominal Variables:

•A variable whose values are used only to name categories

oE.g. Province, Country names

•Also referred to as categorical or qualitative variables

Identifier variables:

•A categorical variable that records an unique value for each case, used

to name or identify it

oE.g. Student ID number

Ch.2 Displaying and describing categorical data:

Bar chart:

•May be used to display the distribution of a categorical variable,

showing the counts for each category next to each other for easy

comparison

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

Pie Chart:

•Shows the whole group of cases as a circle

•Slice the circle into pieces who size is proportional to the fraction of the

whole in each category

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

Contingency tables:

•Two or more categorical variables

•Shows how individuals are distributed along each variables, contingent

on the value of other variable

•Ex:

Gender Smoker Non-Smoker Total

Male 72 44 116

Female 34 53 87

Total 106 97 203

Relative Frequency Contingency Table:

•% Value for cell x = (Count value in cell x / Total number surveyed) x

100

Gender Smoker Non-Smoker

Male (72/203) x 100% =

35.47%

(44/203) x 100% =

21.67%

Female (34/203) x 100% =

16.75%

(53/203) x 100% =

26.11%

Marginal Distribution:

•In the margins of a contingency table, the frequency distribution of one

of the variables

•Either counts or percentages

•Ex:

Gender Smoker Non-Smoker Total

Male (72/203) x 100%

= 35.47%

(44/203) x 100%

= 21.67%

(116/203) x 100% =

57.14%

Female (34/203) x 100%

= 16.75%

(53/203) x 100%

= 26.11%

(87/203) x 100% =

42.86%

Total (106/203) x 100%

= 52.22%

(97/203) x 100%

= 47.78%

(203/203) x 100% =

100%

•Marginal Distribution:

oGender: 57.14% and 42.86%

oSmoker Status: 52.22% and 47.78%

Conditional Distribution:

•Show the distribution of one variable for just those cases that satisfy

condition on another variable

•Ex:

Gender Smoker Non-Smoker Total

Male 72 44 116

Female 34 53 87

Total 106 97 203

•Gender:

o(72/116) x 100% = 62.07%

o(44/116) x 100% = 37.93 %

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