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Intro to Stats

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Types of Statistics
Descriptive Statistics
Examples:
A set of methods used to describe data already collected so that its main features can be seen immediately. eg: averages, sports, EXISTS TODAY AND NOW
Inferential Statistics
Examples:
Techniques that allow us to make a generalization, estimate, or prediction about a population based on a sample. eg: polls, tv ratings, use a sample to predict entire population info

Application: Joe D. Politician is running for Mayor. He calls you on the phone and asks you to find out what percentage of the registered voters in the city will vote for him. What are your options?
Descriptive example: - Call everyone and ask them
Inferential example: - Call 4 people, ask them, and generalize the population (not good) - Take a larger representative example (1000) and generalize to the population

Example 1: Out of 350 randomly selected students from Sheridan College, 280 owned a cell phone.
Summarize this using Descriptive Statistics:
80% of students own a cell phone
Summarize this using Inferential Statistics:
80% of ALL Sheridan students have a cell phone

Example 2: On the last 3 Sundays, Mr. Carsalesman sold 2, 1, and 0 new cars respectively.
Summarize this using Descriptive Statistics:
He sold an average of 1 car every Sunday
Summarize this using Inferential Statistics:
He sells an average of 1 car on ALL Sundays

Test Your Knowledge
The last four semesters an instructor taught Intermediate Algebra, the following numbers of people passed the class.
17 19 4 20
Which of the following conclusions can be obtained from purely descriptive measures and which can be obtained by inferential methods?

The last four semesters the instructor taught Intermediate Algebra, an average of 15 people passed the class. DESCRIPTIVE | Descriptive or Inferential? | | Choose an item. | The next time the instructor teaches Intermediate Algebra, we can expect approximately 15 people to pass the class. INFERENTIAL | Choose an item. | This instructor will never pass more than 20 people in an Intermediate Algebra class. INFERENTIAL | Choose an item. | The last four semesters the instructor taught Intermediate Algebra, no more than 20 people passed the class. DESCRIPTIVE | Choose an item. | Only 5 people passed one semester because the instructor was in a bad mood the entire semester. INFERENTIAL | Choose an item. | The instructor passed 20 people the last time he taught the class to keep the administration off of his back for poor results. INFERENTIAL | Choose an item. | The instructor passes so few people in his Intermediate Algebra classes because he doesn't like teaching that class. INFERENTIAL | Choose an item. |

Types of DATA
Qualitative:
Examples:
Non-numeric or categorical
Hair colour, program, laptop choice, gender, feelings
Quantitative:
Discrete: A variable with a countable number of distinct values (result of counting).
Examples:
Number of siblings

Continuous: A variable that can have any value within an interval (usually a result of measurement).
Examples:
Height of a tree, Money

| Qualitative OR Quantitative? | Discrete OR Continuous? | The manufacturer of your car QUAL | Choose an item. | Choose an item. | Whether a person has a traffic violation QUAL | Choose an item. | Choose an item. | The number of courses you are taking QUAN/DIS | Choose an item. | Choose an item. | The fuel efficiency of your car QUAN/CON | Choose an item. | Choose an item. | The distance from Toronto to Vancouver QUAN/CON | Choose an item. | Choose an item. | The amount of money you earned last month QUAN/CON | Choose an item. | Choose an item. | The length of time waiting in line at Tim Horton’s QUAN/CON | Choose an item. | Choose an item. | Number of insurance claims filed in March QUAN/DIS | Choose an item. | Choose an item. | The different brands of pickles QUAL | Choose an item. | Choose an item. | Number of senior citizens in a hospital waiting room QUAN/DIS | Choose an item. | Choose an item. |

Test Your Knowledge
Categorize each of the following as Qualitative or Quantitative. If it is Quantitative, determine if it is Discrete or Continuous.

Mutually Exclusive:
Example: Following are two different sets of categories that are supposed to identify a user’s age group.
Which of the following best describes your age group? Set 1 | Set 2 | a. Under 21 b. 21 to 25 c. 25 to 35 d. 35 to 45 e. 45 to 55 f. 55 to 65 g. 65 and over | a. Under 21 b. 21 to 24 c. 25 to 34 d. 35 to 44 e. 45 to 54 f. 55 to 64 g. 65 and over |
Which set would be considered “Mutually Exclusive” – Set 1 or Set 2? Choose an item.
Explain:
Set 1 has overlapping categories

Exhaustive: There must be a category in which the observation/measurement falls
Example: Following are two questions that could possibly be found on a survey.
How would you like to receive coupons from our restaurant in the future? Question 1Select all that apply: a. Newspaper b. Magazine c. Mailings | Question 2Select all that apply: a. Newspaper b. Magazine c. Mailings d. Email e. Other, please specify ___________ |

Which question would be considered “Exhaustive”? – Question 1 or Question 2?
Choose an item.
Explain:
Question 2 b/c OTHER CATEGORY

Levels of Measurement
Nominal:
* qualitative (distinguished by name only) * can only be classified and counted * no order to categories * no mathematical operations * ORDER DOES NOT MATTER, QUALITATIVE, MUST BE MUTUALLY EXCLUSIVE
Examples:
Hair colour, Sheridan program, eye colour, mode of transportation
Ordinal
* a natural order exists * qualitative or quantitative VERIFY THIS * distance between values not equal * no mathematical operations
Examples:
1st, 2nd, 3rd places in a race
“strongly agree, agree, neutral, disagree” etc. on a survey
Interval
* a natural order exists * strictly quantitative distance between values is equal and can be measured * a value of “0” is arbitrary * Addition or subtraction
Examples:
Temperature, time of day (1:00pm, noon etc)
Ratio
* a natural order exists * strictly quantitative * distance between values is equal and can be measured * a value of “0” is meaningful * All mathematical operations
Examples:
Money, Physics Displacement, REMEMBER “TWICE AS MUCH” RULE

AGE EXAMPLE:
Ratio: What is your age?
Ordinal: Under 21, between 21 to 39, 49 to 50…

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