Chapter 1: Data Collection – Introduction to Statistics and Types of Data

Chapter 1: Data Collection

Section 1.1: Introduction to the Practice of Statistics

Objective 1 – Define Statistics and Statistical Thinking

Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. It also involves providing a measure of confidence in any conclusions.

• Statistics rests on two major concepts: variation and data.

• Variables are characteristics of individuals within the population.

• Data is information that describes characteristics of an individual.

• Key Point: Variables vary. For example, the heights of all individuals are not the same, which is why statistics is needed to understand and interpret this variation.

Statistics are more than just numbers! Context is key!

How are Mathematics and Statistics Different?

• Statistics focuses on data collection, interpretation, and context, while mathematics emphasizes abstract reasoning and proof.

• Statistics is used in everyday life, such as in news, social media, and personal record-keeping.

Objective 2 – Explain the Process of Statistics

• It is often unreasonable to access all individuals of interest in a study (the population), so a sample is used.

• Population: The entire group to be studied.

• Sample: A subset of the population selected for study.

• Parameter: A numerical summary of a population.

• Statistic: A numerical summary of a sample.

Example: In a study of high school student sleep patterns, the population is all high school students, and the sample is a group of 385 randomly selected students.

1. Identify the research objective.

2. Collect the information needed to answer the questions.

3. Describe the data – organize and summarize the information.

4. Draw conclusions from the data.

Statistical inference is the process of using data from a sample to make estimates or test hypotheses about the characteristics of a population. Results are often reported with a margin of error and a confidence level.

Example: A hospital reports that all car crash victims have an average of $9000 in hospital bills with a margin of error of $266 and a 95% level of confidence.

Objective 3 – Distinguish Between Qualitative and Quantitative Variables

• Qualitative (categorical) variables: Allow for classification of individuals based on some attribute or characteristic (e.g., eye color, gender).

• Quantitative variables: Provide numerical measures of individuals (e.g., age, height).

Example: Classify the following as qualitative or quantitative:

Variable	Type
Colors of automobiles	Qualitative
Numbers on a jersey	Qualitative
Number of seats in a theater	Quantitative
List of house numbers	Qualitative
Age of employees	Quantitative

Example Data Table:

FEMALE	ZIP CODE	AGE	HEIGHT	ACT	INTEREST
0	43015	18	56	20	7
1	44833	19	58	21	8
0	43221	20	60	23	9
1	43210	21	62	25	10

• How many variables are there? 6

• How many people were surveyed? 4

• Is FEMALE numerical or categorical? Categorical (coded as 0/1)

• Is AGE numerical or categorical? Numerical

Objective 4 – Distinguish Between Discrete and Continuous Variables

• Discrete variable: A quantitative variable with a finite or countable number of possible values (e.g., number of siblings).

• Continuous variable: A quantitative variable with an infinite number of possible values, often measured (e.g., height, weight).

Example: Determine if the following are discrete or continuous:

Value	Discrete	Continuous
Honda Civic has 4 cylinders	✔
George Washington was 188 cm tall		✔
House of Representatives has 435 members	✔
Arm circumference of 27.5 cm		✔
Earthquake measurement of 0.70		✔

Objective 5 – Determine the Level of Measurement of a Variable

• Nominal: Data are labels or names; cannot be arranged in order (e.g., eye color).

• Ordinal: Data can be arranged in order, but differences are meaningless (e.g., ranks).

• Interval: Differences are meaningful, but ratios are not; no true zero (e.g., temperature in Celsius).

• Ratio: Ratios are meaningful; there is a true zero (e.g., heights, weights).

Level of Measurement	Brief Description	Example
Ratio	Natural zero; ratios are meaningful	Heights, weights, distances
Interval	Differences meaningful; no natural zero	Body temperatures in Celsius
Ordinal	Can be arranged in order; differences not meaningful	Ranks of colleges
Nominal	Names, labels, categories only	Eye colors

Example: Identify the level of measurement for:

• Hair color of women on a tennis team – Nominal

• Numbers on shirts of a soccer team – Nominal

• Ages of students – Ratio

• Temperatures in degrees Fahrenheit – Interval

• Number of milligrams of tar in cigarettes – Ratio

• Number of pages in a book – Ratio

• Marriage status – Nominal

• List of social security numbers – Nominal

• Movie ratings from "poor" to "excellent" – Ordinal

• Final grades (A, B, C, D, F) – Ordinal

• Annual salaries – Ratio

• List of zip codes – Nominal

Summary

• Statistics is the science of data collection, analysis, and interpretation.

• Variables can be qualitative or quantitative, discrete or continuous.

• Levels of measurement (nominal, ordinal, interval, ratio) determine the appropriate statistical methods.