Statistics Exam Notes

Explain the importance of statistical knowledge.
Define statistics and provide examples of its application.
Differentiate between descriptive and inferential statistics.
Classify variables as qualitative or quantitative, and discrete or continuous.
Distinguish between nominal, ordinal, interval, and ratio levels of measurement.
List the values associated with the practice of statistics.

Data is collected everywhere, requiring statistical knowledge to make the information useful.
Statistical techniques are used in professional and personal decisions.
Knowledge of statistics is needed to understand the world and be conversant in your career.
Statistics helps in making more effective personal and professional decisions.

Statistics is more than presenting numerical facts.
- Example: Inflation rate for the calendar year was 0.7%. Statistics can be applied to compare this year's inflation rate to past observations, determining if it is higher, lower, or about the same, and identifying trends.
Definition: Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions.

Used to organize data into a meaningful form.
Summarizes data and provides information that is easy to understand.
- Example: There are a total of 46,837 miles of interstate highways in the U.S. The interstate system represents 1% of the nation's roads but carries more than 20% of the traffic. Texas has the most interstate highways, and Alaska doesn’t have any.
Definition: Methods of organizing, summarizing, and presenting data in an informative way.

Population: The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest.
Sample: A portion or part of the population of interest.

Used to estimate properties of a population.
Allows making decisions based on a limited set of data.
- Example: TV networks monitor the popularity of their programs using Nielsen to sample TV viewer preferences. 9% of a sample of households with television watched The Big Bang Theory during the week of November 2, 2015.
Definition: The methods used to estimate a property of a population based on a sample.

An object or individual is observed and recorded as a non-numeric characteristic or attribute.
- Examples: gender, state of birth, eye color.

A variable that is reported numerically.
- Examples: balance in your checking account, the life of a car battery, the number of people employed by a company.

Typically the result of counting.
Values have “gaps” between the values.
- Examples: the number of bedrooms in a house, the number of students in a statistics course.

Usually the result of measuring something.
Can assume any value within a specific range.
- Examples: the air pressure in a tire, duration of flights from Orlando to San Diego.

Qualitative: Brand of PC, marital status, hair color
Quantitative:
- Discrete: Children in a family, strokes on a golf hole, TV sets owned
- Continuous: Amount of income tax paid, weight of a student, yearly rainfall in Tampa, FL

Four levels of measurement: nominal, ordinal, interval, and ratio.
The level of measurement determines the type of statistical analysis that can be performed.

The lowest level of measurement.
Data is represented as labels or names.
They have no order.
They can only be classified and counted.
- Examples: classifying M&M candies by color, identifying students at a football game by gender.
  Note: You can consider $gender$ as an example.

Based on a relative ranking or rating of items based on a defined attribute or qualitative variable.
Variables based on this level of measurement are only ranked and counted.
- Examples: the list of top ten states for best business climate, student ratings of professors.

This data has all the characteristics of ordinal level data plus the differences between the values are meaningful.
There is no natural 0 point.
- Examples: the Fahrenheit temperature scale, dress sizes.
The interval level of measurement is based on a scale with a known unit of measurement.
It's important to note that $0^\circ F$ does not mean there is no temperature.

The highest level of measurement.
The data has all the characteristics of the interval scale and ratios between numbers are meaningful.
The 0 point represents the absence of the characteristic.
- Examples: wages, changes in stock prices, and weight.

Nominal: Data may only be classified (e.g., jersey numbers of football players, make of car).
Ordinal: Data are ranked (e.g., your rank in class, team standings in the Southeastern Conference).
Interval: Meaningful difference between values (e.g., temperature, dress size).
Ratio: Meaningful 0 point and ratio between values (e.g., number of patients seen, number of sales calls made, distance to class).

Practice statistics with integrity and honesty when collecting, organizing, summarizing, analyzing, and interpreting numerical information.
Maintain an independent and principled point of view when analyzing and reporting findings and results.
Question reports that:
- are based on data that do not fairly represent the population.
- do not include all relevant statistics.
- introduce bias in an attempt to mislead or misrepresent.