1. Math 220: Elementary Statistics
Ty Darensburg-Crane, MS

2. Introductions & Syllabus
From New Orleans, LA
Education
Bachelor’s in Mathematics and Computer Science from Xavier University of Louisiana
Master’s in Biostatistics from Emory University
+10 years educational experience
Math software company
Teaching HS to graduate school level
Director of Math XU
Important notes from the Syllabus

3. Chp 1: The Nature of Probability & Statistics
Statistics: science of conducting studies to collect, organize, summarize, analyze and draw conclusions from data
Why study statistics?
If you have to conduct research of your own or prepare a report
To read and understand studies performed in your field
To be a better informed consumer and citizen

4. Terminology
Variable: characteristic that can assume different values (i.e. age, height, etc.)
Data: values that variables can assume (variables whose values are determined by chance are called random variables)
What would be an example of a random variable?
Gender
Value of a fair die thrown, etc.

5. Stats…not just numbers
Data
Qualitative
Quantitative
Discrete
Continuous
Variables and Types of Data:
Quantitative: numerical data
Qualitative: variables that can be placed in categories

6. Statistics is more than just numbers…
Quantitative: numerical data “think quantity”
Discrete: can be counted (i.e. age)
Continuous: assume an infinite number of values, and often include fractions and decimals (i.e. weight)
Qualitative: variables that can be placed into distinct categories, sometimes called categorical

7. Classify the following data
Quantitative or Qualitative?
Number of children in a family
Quantitative
Discrete
Gender
Qualitative
Time taken to run a mile
Continuous

8. Collecting data A popular way to collect data - survey
Three major types are telephone, mailed questionnaire, and personal interview:
Telephone
Advantages: not costly, anonymous feel
Disadvantages: do not reach unlisted numbers, people do not answer
Mailed Questionnaire
Advantages: can cover wider geographic area, not expensive, anonymous
Disadvantages: people do not open mail or return surveys

9. Collecting Data
Three major types are telephone, mailed questionnaire, and personal interview:
Personal interview
Advantages: in-depth responses
Disadvantages: not time/cost effective, interviewers must be trained in asking questions/recording responses, bias

10. Population v. Sample
It can be impossible to include the entire population. To ensure that studies are as accurate as possible, statisticians use special sampling techniques
Population: all subjects that are being studied
Sample: group of subjects selected from a population

11. Sampling techniques
Random: selected by using chance methods (drawing names out of hat)
Systematic: numbering each subject of the population and selecting every kth subject (selecting every 3rd student in roll book)
Stratified: dividing population into groups based on some characteristic and sampling from each group randomly (split class by gender, randomly select 5 from each group)

12. Sampling techniques (cont.)
Cluster: dividing population based on geographic area then randomly selecting clusters and surveying all members of cluster (pick 5 random UIU classes and survey all students
Convenience: selects subjects that are convenient (subjects at a festival) – must be taken with care so that it is representative

13. Uses and Misuses of Statistics
Statistics are sometimes misused to sell products that don’t work
or attempt to prove something that really isn’t true
Here are some common ways this is done:
Suspect samples: size and source of sample
Changing the subject: using different values to represent the same data (i.e. percent vs. actual amount)
Detached statistics: using a statistic where no comparison is made
Match each scenario to a label on the left:
Rapid release Tylenol works 4 times faster.
Detached statistic
9 out of 10 women prefer Dove soap
Suspect sample
I’m going to double your salary! Or your salary will increase by $0.
Changing the subject

14. Uses and Misuses of Statistics
Here are some common ways this is done:
Implied connection: claims that imply connections between variables that may not exist (look for words like “may”, “some people”, and “might help”)
Faulty survey questions: questions improperly written
Match each scenario to a label on the left:
Eating dairy products three times a day may help you lose weight.
Implied connection
Are you in favor of a special tax to provide national healthcare?
Faulty survey questions
Studies suggest that appemine decreases hunger in some people

15. Chp 2: Frequency Distributions & Graphs
After data is collected it must be organized
The most useful method of presenting data is by constructing statistical charts and graphs
We will discuss how to construct frequency distributions, pie charts, and time series graphs

16. Frequency Distributions
Frequency distribution: organization of raw data in table form using classes and frequencies
Ex army inductees were given a blood test to determine their blood type. The data set is (p. 38):
A B B AB O
O O B AB B
B B O A O
A O O O AB
AB A O B A

17. Frequency Distributions
Ex 2. Record high temperatures for each of the 50 states (p. 41) When data is not already in categories you can create classes (categories). For our purposes we will typically use 5 to 10 classes. Step 1: Determine the classes. Use 7 classes for this example. Largest – Smallest value = =34 Take result and divide by number of classes = 34/7=4.9 Round up ≈ 5, This is your class width Step 2: Create frequency distribution using class width

18. Histogram Visual representation of frequency distribution
Let’s revisit Example 2 with record high temperatures.

19. Time Series Graphs
When data are collected over a period of time, they can be represented by a time series graph
Ex 3. Workplace Homicides (p.72)
Year
‘03
‘04
‘05
‘06
‘07
‘08
Number
632
559
567
540
628
517

20. Pie Charts Ex 4. Super Bowl Snacks Snack Pounds Potato Chips
11.2 million
Tortilla Chips
8.2 million
Pretzels
4.3 million
Popcorn
3.8 million
Snack nuts
2.5 million
Total
30 million

21. Pie Charts Ex 4. Super Bowl Snacks Snack Pounds Percentage
Potato Chips
11.2 million
11.2/30=.373≈37.3%
Tortilla Chips
8.2 million
8.2/30=.273≈27.3%
Pretzels
4.3 million
4.3/30=.143≈14.3%
Popcorn
3.8 million
3.8/30=.127≈12.7%
Snack nuts
2.5 million
2.5/30=.083≈8.3%
Total
30 million