This document provides an overview of key concepts in statistics including: - Descriptive statistics which summarize and describe data, and inferential statistics which make predictions based on samples. - The difference between a population, which is all subjects being studied, and a sample, which is a subset selected from the population. - Types of variables like qualitative, quantitative, discrete, continuous and different measurement scales. - Various data collection methods like random, systematic, stratified and cluster sampling. - The two main types of statistical studies - observational which observes phenomena, and experimental which manipulates variables. - Common statistical terms like independent and dependent variables and misuses of statistics to mislead.

1. Quote of the Day
Oh, people can come up with statistics to
prove anything. 14% of people know
that. ---Homer Simpson
What are Statistics?

2. Chapter 1:The Nature of
Probability and Statistics
Section 1:
Descriptive and Inferential
Statistics

3. Stats in Daily Life
 Of the people in the US, 14% said they feel
happiest in June, and 14% said they feel
happiest in December.
 The average in-state college tuition and fees
for 4-year pubic college is $5,836.
 Every day in the US about 120 golfers claim
that they made a hole-in-one.
 4 out of 5 doctors leaves one doctor.- Chevy
Chase

4. What is Statistics?
 The science of conducting studies to
collect, organize, summarize, analyze
and draw conclusions from data.

5. What is Data?
 The values that the variables can
assume.
 A collection of values forms a Data
Set
 Each Value in the data set is called:

Data Value or
 Datum

6. What is a variable?
 A characteristic or attribute that can
assume different values.

7. Types of Statistics
1. Descriptive Statistics
 Consists of the collection, organization,
summarization, and presentation of data
 Ex: Government Census
 Taken every ten years

Describes average income, family size, etc..
 What does this mean?
 Basically used to describe a situation.

8. Types of Statistics
2. Inferential Statistics
 Consists of generalizing from samples
to populations, performing estimations
and hypothesis tests, determining
relationships among variables, and
making predictions.

Ex: Winning the lottery
 1 in a million
 What does this mean ?
 Used to predict the outcome of an event.

9. What is the difference between a
Population and a Sample?
 Population- consists of all subjects
that are being studied.
 Sample- is a group selected from a
population.

10. Population
Sample

11. Assignment
 Page 26
 #’s 1-6

12. Section 2: Types of Variables
 Qualitative Variables:
 Variables that can be placed into distinct
categories, according to some
characteristic or attribute.
 Ex: Gender, Eye color, Geographic
Location

13. 2 Types of Variables
 Quantitative Variables:
 Variables that are numerical and can be
ordered or ranked.
 Ex: Age, height, weight, body temp
 Classified by two groups
 Discrete Variables
 Continuous Variables

14. Practice
 Page 26 #8

15. Discrete Variables
 Assume values that can be counted
 Assigned numbers such as 0,1,2,3,…
 Ex:
 # of children
 # of students

16. Continuous Variables
 Can assume an infinite number of
values between any two specific values.
 Obtained by measuring
 Often include fractions and decimals.
 Ex:
 Temperature
 Time
 Length

17. Practice
 Page 27 #9

18. Measurement Scale
 Used to categorize, count, or measure
variables.
 Types:
 Nominal
 Ordinal
 Interval
 Ratio

19. Nominal Level of Measurement
 Classifies data into mutually exclusive,
exhausting categories in which no order
or ranking can be imposed on the data.
 Ex:
 Male/Female
 Single/Married/Divorced/Widowed/Separated
 Democratic/Republican

20. Ordinal Level of Measurement
 Classifies data into categories that can
be ranked; however, precise differences
between the ranks do not exist.
 Ex:
 Letter Grades (A, B, C, D, F)
 1st, 2nd, 3rd, etc
 Small, Medium, Large
 Freshman, Sophomores, Juniors, Seniors

21. Interval Level of Measurement
 Ranks data, and precise differences
between units of measures do exist:
however, there is no meaningful zero.
 Ex:
 Temperature: 72°F and 73°F, difference of
1°F, but 0°F does not mean no heat
present
 IQ: 109 and 110, difference of 1 point, but
0 does not mean there is no intelligence.

22. Ratio Level of Measurement
 Possesses all the characteristics of interval
measurements, and there exists a true zero.
 In addition, true ratios exists when the same
variables is measured on two different
members of the population.
 Ex:
 Salary
 Time
 Age

23. Practice
 Page 26 #7

24. Section 3: Data Collection and
Sampling Techniques.
 Types:
 Random
 Systematic
 Stratified
 Cluster

25. Random Sampling
 Selection based on chance or random
numbers.
 Procedure:
 Assign number to each subject in
population
 Select numbers at random from “hat”

26. Random Sampling
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21

27. Systematic Sampling
 Procedure:
 Number each subject in population
 Select every kth subject
 Example:
 Population: 100 Sample: 10
 Kth term: 100/10=10
 1, 11, 21, 31, 41, 51, 61, 71, 81, 91

28. Systematic Sampling
Population: 21 Sample: 7
21/7=3: kth term is 3.
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21

29. Stratified Sampling
 Procedures:
 Population divided into groups called:
Strata
 Groups have common characteristic
needed for study.
 Samples randomly selected from each
strata

30. Stratified Sampling

31. Cluster Sampling
 Population is divided into groups called:
Clusters
 Select some clusters
 Survey every member of the cluster for
sample
 Used with large populations

32. Cluster Sampling

33. Other sampling methods
 Convenience sampling
 Use subjects that are convent
 Ex: asking people as they enter the mall
 Sequential sampling
 Double sampling
 Multistage sampling

34. Convenience Sampling
Do you want to
take a survey?

35. Practice
 Page 27 #12

36. Section 4: 2 Types of Studies
 Observational Study
 Researchers merely observe what is
happening or what has happened in the
past
 Try to draw conclusions based on these
observations.
 Ex: studying creatures in the wild
 “Meerkat Manor”

37. Section 4: 2 Types of Studies
 Experimental study
 Researchers manipulate one of the
variables
 Tries to determine how to the manipulation
influences other variables.
 Ex: New medication and placebos

38. Practice
 Page 27-28 #17

39. Statistical Studies include….
 Independent variables
 In an experimental study is the one that is
being manipulated by the researcher.
 Also called: Explanatory variable
 Dependent variables
 Resultant variable
 Also called: Outcome variable

40. Misuses of Statistics
 Suspect Samples
 Too small
 Convenience
 Volunteers
 Changing the subject
 Increase of 3%
 Increase of $600,000

41. Misuses of Statistics
 Detached Statistics- no comparison
 “Works 5 times faster”
 “1/3 fewer calories”
 Implied Connection
 “Eating fish may help you achieve better in
school”

42. Misuses of Statistics
 Misleading Graphs- Chapter 2
 Faulty Survey Questions
 “Do you feel there should be a 4 day
school week?”
 “Do you feel there should be a 4 day
school week from 4 am to midnight?”

43. Section 1-6: Computers and
Calculators
 Computer and Calculators GOOD

44. End of Chapter 1