1. Introduction to Statistics
Chapter 1
Introduction to Statistics
1-1 Overview
1- 2 Types of Data
1- 3 Abuses of Statistics
1- 4 Design of Experiments

2. Statistics (Definition)
Overview
Statistics (Definition)
A collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data

3. Definitions Population Sample
The complete collection of all data to be studied.
Sample
The subcollection data drawn from the population.

4. Example Identify the population and sample in the study
A quality-control manager randomly selects 50 bottles of Coca-Cola to assess the calibration of the filing machine.
Emphasize that a population is determined by the researcher, and a sample is a subcollection of that pre-determined group. For example, if I collect the ages from a section of elementary statistics students, that data would be a sample if I am interested in studying ages of all elementary statistics students. However, if I am studying only the ages of the specific section of elementary statistics, the data would be a population.

5. Definitions Statistics Descriptive Statistics Broken into 2 areas
Inferencial Statistics

6. Definitions Descriptive Statistics Inferencial Statistics
Describes data usually through the use of graphs, charts and pictures. Simple calculations like mean, range, mode, etc., may also be used.
Inferencial Statistics
Uses sample data to make inferences (draw
conclusions) about an entire population
Emphasize that a population is determined by the researcher, and a sample is a subcollection of that pre-determined group. For example, if I collect the ages from a section of elementary statistics students, that data would be a sample if I am interested in studying ages of all elementary statistics students. However, if I am studying only the ages of the specific section of elementary statistics, the data would be a population.
Test Question

7. 1-2 Types of Data Parameter vs. Statistic
Quantitative Data vs. Qualitative Data
Discrete Data vs. Continuous Data

8. Definitions Parameter population parameter
a numerical measurement describing some characteristic of a population
population
parameter

9. Definitions Statistic sample statistic
a numerical measurement describing some characteristic of a sample
sample
statistic

10. Examples Parameter Statistic
51% of the entire population of the US is Female
Statistic
Based on a sample from the US population is was determined that 35% consider themselves overweight.

11. Definitions Quantitative data
Numbers representing counts or measurements
Qualitative (or categorical or attribute) data
Can be separated into different categories that are distinguished by some nonnumeric characteristics

12. Examples Quantitative data
The number of FLC students with blue eyes
Qualitative (or categorical or attribute) data
The eye color of FLC students

13. Definitions
We further describe quantitative data by distinguishing between discrete and continuous data
Discrete
Quantitative Data
Continuous

14. Definitions Discrete Continuous
data result when the number of possible values is either a finite number or a ‘countable’ number of possible values
0, 1, 2, 3, . . .
Continuous
(numerical) data result from infinitely many possible values that correspond to some continuous scale or interval that covers a range of values without gaps, interruptions, or jumps
Understanding the difference between discrete versus continuous data will be important in Chapters 4 and 5.
When measuring data that is continuous, the result will be only as precise as the measuring device being used to measure. 2 3

15. Examples
Discrete
The number of eggs that hens lay; for example, 3 eggs a day.
Continuous
The amounts of milk that cows produce; for example, gallons a day.

16. Definitions Univariate Data Bivariate Data
Involves the use of one variable (X)
Does not deal with causes and relationship
Bivariate Data
Involves the use of two variables (X and Y)
Deals with causes and relationships
Understanding the difference between discrete versus continuous data will be important in Chapters 4 and 5.
When measuring data that is continuous, the result will be only as precise as the measuring device being used to measure.

17. Example Univariate Data Bivariate Data
How many first year students attend FLC?
Bivariate Data
Is there a relationship between then number of females in Computer Programming and their scores in Mathematics?
Understanding the difference between discrete versus continuous data will be important in Chapters 4 and 5.
When measuring data that is continuous, the result will be only as precise as the measuring device being used to measure.

18. Important Characteristics of Data
1. Center: A representative or average value that indicates where the middle of the data set is located
2. Variation: A measure of the amount that the values vary among themselves or how data is dispersed
3. Distribution: The nature or shape of the distribution of data (such as bell-shaped, uniform, or skewed)
4. Outliers: Sample values that lie very far away from the vast majority of other sample values
5. Time: Changing characteristics of the data over time
Most important characteristics necessary to describe, explore, and compare data sets.
page 34 of text

19. Uses of Statistics
Almost all fields of study benefit from the application  of statistical methods
Sociology, Genetics, Insurance, Biology, Polling, Retirement Planning, automobile fatality rates, and many more too numerous to mention.
page 11 of text

20. 1-3 Abuses of Statistics Bad Samples Small Samples Loaded Questions
Misleading Graphs
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
Deliberate Distortions

21. Abuses of Statistics Bad Samples
Inappropriate methods to collect data. BIAS (on test) Example: using phone books to sample data.
Small Samples (will have example on exam)
We will talk about same size later in the course. Even large samples can be bad samples.
Loaded Questions
Survey questions can be worked to elicit a desired response

22. Abuses of Statistics Bad Samples Small Samples Loaded Questions
Misleading Graphs
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
Deliberate Distortions

23. Salaries of People with Bachelor’s Degrees and with High School Diplomas
$40,500
$40,500
$40,000
$40,000
35,000
30,000
$24,400
30,000
20,000
$24,400
page 11 of text
Graphs whose vertical scales do not start at 0 will give a misleading representation of the differences in heights of the bars.
25,000
10,000
20,000
Bachelor High School
Degree Diploma
Bachelor High School
Degree Diploma
(a)
(test question)
(b)

24. We should analyze the numerical information given in the graph instead of being mislead by its general shape.

25. Abuses of Statistics Bad Samples Small Samples Loaded Questions
Misleading Graphs
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
Deliberate Distortions

26. Double the length, width, and height of a cube, and the volume increases by a factor of eight
What is actually intended here? 2 times or 8 times?
page 14 of text

27. Abuses of Statistics Bad Samples Small Samples Loaded Questions
Misleading Graphs
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
Deliberate Distortions

28. Abuses of Statistics Precise Numbers
There are 103,215,027 households in the US. This is actually an estimate and it would be best to say there are about 103 million households.
Distorted Percentages
100% improvement doesn’t mean perfect.
Deliberate Distortions
Lies, Lies, all Lies

29. Abuses of Statistics Bad Samples Small Samples Loaded Questions
Misleading Graphs
Pictographs
Precise Numbers
Distorted Percentages
Partial Pictures
Deliberate Distortions

30. Abuses of Statistics Partial Pictures
“Ninety percent of all our cars sold in this country in the last 10 years are still on the road.”
Problem: What if the 90% were sold in the last 3 years?

31. 1-4 Design of Experiments

32. Definition Experiment Event apply some treatment (Action)
observe its effects on the subject(s) (Observe)
Example: Experiment: Toss a coin
Event: Observe a tail

33. Designing an Experiment
Identify your objective
Collect sample data
Use a random procedure that avoids bias
Analyze the data and form conclusions

34. Methods of Sampling Random (type discussed in this class) Systematic
Convenience
Stratified
Cluster
review of the 5 different types of sampling

35. Definitions Random Sample Simple Random Sample (of size n)
members of the population are selected in such a way that each has an equal chance of being selected (if not then sample is biased)
Simple Random Sample (of size n)
subjects selected in such a way that every possible sample of size n has the same chance of being chosen

36. Random Sampling - selection so that each has an equal chance of being selected
page 19 of text

37. Systematic Sampling Select some starting point and then
select every K th element in the population

38. use results that are easy to get
Convenience Sampling
use results that are easy to get

39. subdivide the population into at
Stratified Sampling
subdivide the population into at
least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum)

40. Cluster Sampling - divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters
Students will most often confuse stratified sampling with cluster sampling. Both break the population into strata or sections. With stratified a few are selected from each strata. With cluster, choose a few of the strata and choose all the member from the chosen strata.

41. Definitions Sampling Error Nonsampling Error
the difference between a sample result and the true population result; such an error results from chance sample fluctuations.
Nonsampling Error
sample data that are incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective instrument, or copying the data incorrectly).
page 23 of text

42. Using Formulas Factorial Notation Order of Operations
8! = 8x7x6x5x4x3x2x1
Order of Operations
( )
POWERS
MULT. & DIV.
ADD & SUBT.
READ LIKE A BOOK
Keep number in calculator as long a possible
page 23 of text