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Lesson 2Exploring Data with Graphs

- Learn ….

The Different Types of Data

The Use of Graphs to Describe

Data

Section 2.1

What are the Types of Data?

In Every Statistical Study:

- Questions are posed
- Characteristics are observed

Characteristics are Variables

A Variable is any characteristic that is recorded for subjects in the study

Variation in Data

- The terminology variablehighlights the fact that data values vary.

Example: Students in a Statistics Class

- Variables:
- Age
- GPA
- Major
- Smoking Status
- …

Data values are called observations

- Each observation can be:
- Quantitative
- Categorical

Categorical Variable

- Each observation belongs to one of a set of categories
- Examples:
- Gender (Male or Female)
- Religious Affiliation (Catholic, Jewish, …)
- Place of residence (Apt, Condo, …)
- Belief in Life After Death (Yes or No)

Quantitative Variable

- Observations take numerical values
- Examples:
- Age
- Number of siblings
- Annual Income
- Number of years of education completed

Graphs and Numerical Summaries

- Describe the main features of a variable
- For Quantitative variables: key features are center and spread
- For Categorical variables: key feature is the percentage in each of the categories

Discrete

- A quantitative variable is discrete if its possible values form a set of separate numbers such as 0, 1, 2, 3, …

Examples of discrete variables

- Number of pets in a household
- Number of children in a family
- Number of foreign languages spoken

Continuous

- A quantitative variable is continuous if its possible values form an interval

Examples of Continuous Variables

- Height
- Weight
- Age
- Amount of time it takes to complete an assignment

Frequency Table

- A method of organizing data
- Lists all possible values for a variable along with the number of observations for each value

Example: Shark Attacks

Example: Shark Attacks

- What is the variable?
- Is it categorical or quantitative?
- How is the proportion for Florida calculated?
- How is the % for Florida calculated?

Example: Shark Attacks

- Insights – what the data tells us about shark attacks

Identify the following variable as categorical or quantitative:

Choice of diet

(vegetarian or non-vegetarian):

- Categorical
- Quantitative

Identify the following variable as categorical or quantitative:

Number of people you have known who have been elected to political office:

- Categorical
- Quantitative

Identify the following variable as discrete or continuous:

The number of people in line at a box office to purchase theater tickets:

- Continuous
- Discrete

Section 2.2

How Can We Describe Data Using Graphical Summaries?

Graphs for Categorical Data

- Pie Chart: A circle having a “slice of pie” for each category
- Bar Graph: A graph that displays a vertical bar for each category

Pie Chart vs. Bar Chart

- Which graph do you prefer?
- Why?

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