1. Introduction to Statistics

2. Learning Goal:
Define Statistics and understand its applications in the real world.
Differentiate between Inferential & Descriptive Statistics.
Differentiate between a parameter and a statistic.

3. Statistics
The science of collecting, analyzing, and drawing conclusions from data.
Where do we encounter statistics in every day life?
Why are they important?
Assignment: Statistics Artifact

4. Two Types of Statistics
Inferential Statistics
Descriptive Statistics

5. Descriptive Statistics
The methods of organizing and summarizing data. Collect and present data through graphical and numerical methods. Look for patterns in data and summarize.
Examples:
Take a poll, present the results.
A certain high school’s graduation rate
Mrs. Lowery’s class data

6. Inferential Statistics
Involves making generalizations from a sample to a population.
Collect data, generalize results to whole population by making an inference.
Examples:
2/3 of all high school student engage in underage drinking
One in five adults have a sexually transmitted disease

7. Population
The entire collection of individuals or objects being studied.

8. Sample A subset of the population.
Used to draw conclusions (make inferences) about the general population.
Example: I want to study high school students study habits.
Population: All high school students
Sample: 500 high school students at BCHS

9. Variable
Any characteristic whose value may change/vary from one individual to another.
What we are studying!
Examples:
SAT scores of students
Diameters of tires
Party affiliations of voters
Sizes of T-shirts

10. Parameter vs. Statistic
Parameter: A numerical value that summarizes the entire population. It a true value!
Statistic: A numerical value that summarizes the sample. True for the sample only!
Example:
40% of all BC students are on free/reduced lunch. 40% is a parameter.
Choose 200 students and find that 38% are on free/reduced lunch. 38% is a statistic.

11. Why do we sample? Brainstorm!!!
Get into your groups and give an example where we would want to sample rather than survey the entire population.

12. Data
Observations of a variable of interest.
Measurements

13. Experiment
How we collect data
Planned activity to yield a set of data

14. Example
A statistics student is interested in finding out something about the average dollar value of cars owned by the faculty members of Brookland-Cayce High School. Each of the terms described can be identified in this situation.
1. Population: the collection of cars owned by all BCHS faculty members.
2. Sample: any subset of that population. For example, the cars owned by the mathematics department is a sample. Can you give me another example?
3. Variable: the dollar value of each individual car.
4.Data: are the set of values associated with the sample we obtained. For example, Ms. Cox’s car is worth $15,000, so it is a data value within our data set.
5. Experiment: consists of the methods used to select the cars that form the sample and to determine the value of each car in the sample. It could be carried out by questioning each member of the mathematics department, or in other ways.
6. Parameter: about which we are seeking information is the average value of all cars of BCHS faculty.
7. Statistic: that will be found is the average value of the cars in the sample.

15. Discuss…
Now, what if a seconds sample were taken? Would we still have the same statistic? What if we sample all the administrators or say, the English department?

16. Assignment:
Bring in one article from the internet, newspaper, or magazine that is an example of Statistics based on what we have discussed today.
Be prepared to discuss the article using the terms we learned today.

17. Article Jigsaw
Get into your groups and share your articles. On a separate sheet of paper try to identify the following for each article:
Population
Sample
Experiment
Variable
Data
Statistic
Parameter
You may not be able to identify all of these!

18. Types of Variables
Categorical/Qualitative
Numerical/Quantitative

19. Categorical Variables
Can be called qualitative or categorical.
Identifies basic differentiating characteristics of the population.
Examples:
Hair color
Eye color
Favorite music

20. Numerical Variables Can be called quantitative or numerical.
Observations or measurements that take numerical values.
RULE OF THUMB: Does it make sense to average the number?
Examples:
Number of students in Mrs. Lowery’s classes
High school graduation rate

21. Practice Income of Columbia households Color of M&M candies
NUMERICAL
Color of M&M candies
CATEGORICAL
Number of speeding tickets this class has had
Area codes in South and North Carolina

22. Numerical Variables Can be divided into 2 groups: Discrete Continuous
Categorical
Numerical
Discrete
Continuous

23. Discrete Variables Can be counted Have gaps between values Examples:
Number of students in classes at BC
Shoe size

24. Continuous Variables Can assume any value along a range of numbers.
Are often measurements of things.
Cannot be counted!
Examples:
Temperature
Height

25. Practice Weights of fire fighters
CONTINUOUS
Flip 4 coins and count the number of heads
DISCRETE
Number of football players with head injuries
Length of snakes in the Riverbanks Zoo reptile house

26. Levels of Measurement 4 Levels of Measurement for Variables
1. Nominal
2. Ordinal
3. Interval
4. Ratio
Ratio is the highest level of measurement

27. Nominal Level The prefix NOM in Latin means Name
This level of measurement classifies data into mutually exclusive categories where no order or ranking can be imposed!
Can NOT be ranked!!!!!

28. Ordinal Level The prefix ORD stands for Order
This level of measurement classifies data into categories that CAN be ranked!

29. Interval Level
This level of measurement is used to classify data that is numerical and has no true zero.
No true zero means that it can take negative values (Zero does not mean anything!)
Example:
Temperature

30. Ratio Level
This level of measurement is used to classify data that is numerical and HAS a true zero.
Does not take negative values, and zero is the absolute bottom!
Hint: If it is not Ratio, it is Interval, and vise versa!

31. Questions to ask yourself…
Is it a number or a category?
Number
Category
Can it be negative?
Can I rank it?
YES NO
YES NO
INTERVAL
RATIO
ORDINAL
NOMINAL

32. Practice Zip Code NOMINAL Grade (A, B, C, D, F) ORDINAL Time RATIO
Weight
Temperature
INTERVAL
NCAA Basketball Rankings ORDINAL
Nationality
Political Affiliation
Age
Salaries

33. Assignment
Intro to Statistics Worksheet