Unit 2: Exploring Data Name 1 Variables and their Graphs

What is the difference between a categorical and a quantitative variable?

Do we ever use numbers to describe the values of a categorical variable? Give some examples.

What is a distribution?

Example: US Census Data

Here is information about 10 randomly selected US residents from the 2000 census.

1. 
   Who are the individuals in this data set?
   

2. 
   What variables are measured? Identify each as categorical or quantitative. In what units were the quantitative variables measured?
   

3. 
   Describe the individual in the first row.
   

What graphs are used for categorical data?

What is the most important thing to remember when making pie charts and bar graphs? Why do statisticians prefer bar graphs?

What is wrong with these graphs?

What is a marginal distribution?

What is a conditional distribution?

The conditional distribution of political preference, conditional on being male:

The conditional distribution of political preference, conditional on being female:

What is the conditional relative frequency distribution of gender among conservatives?

What graphs are used to display quantitative data?

Example: Make a stemplot for the following data,

The following data are price per ounce for various brands of dandruff shampoo at a local grocery store.

0.32 0.21 0.29 0.54 0.17 0.28 0.36 0.23

Can you make a stemplot with this data?

What is the most important thing to remember when making a stemplot?

Example: Tobacco use in G-rated Movies

Total tobacco exposure time (in seconds) for Disney movies:

223 176 548 37 158 51 299 37 11 165 74 9 2 6 23 206 9

Total tobacco exposure time (in seconds) for other studios’ movies:

205 162 6 1 117 5 91 155 24 55 17

Make a back-to-back stemplot.
Boxplots:

Example: We will use the following data representing tornadoes per year in Oklahoma from 1995 until 2004 (Sullivan, 2nd edition, p. 167), to construct a modified box plot .

Briefly describe/illustrate the following distribution shapes:

Identify the shape of the following distributions:

Example: Smart Phone Battery Life

What will cause you to lose points on tests and projects (and cause Miss Hartman to go crazy…or crazier)?

Example: McDonald’s Beef Sandwich__Fat_(g)'>Sandwiches

Here is data for the amount of fat (in grams)

for McDonald’s chicken sandwiches. Are

there any outliers in this distribution?

Draw parallel boxplots for the beef and chicken sandwich data. Compare these distributions.

Example: Energy Cost: Top vs. Bottom Freezers

How do the annual energy costs (in dollars) compare for refrigerators with top freezers and refrigerators with bottom freezers? The data below is from the May 2010 issue of Consumer Reports.

Example: Which gender is taller, males or females? A sample of 14-year-olds from the United Kingdom was randomly selected using the CensusAtSchool website. Here are the heights of the students (in cm). Make a back-to-back stemplot and compare the distributions.

Male: 154, 157, 187, 163, 167, 159, 169, 162, 176, 177, 151, 175, 174, 165, 165, 183, 180

Female: 160, 169, 152, 167, 164, 163, 160, 163, 169, 157, 158, 153, 161, 165, 165, 159, 168, 153, 166, 158, 158, 166

What does the standard deviation measure?

What are some similarities and differences between the range, IQR, and standard deviation?

How is the standard deviation calculated? What is the variance?

What are some properties of the standard deviation?

Example: A random sample of 5 students was asked how many minutes they spent doing HW the previous night. Here are their responses (in minutes): 0, 25, 30, 60, 90. Calculate and interpret the standard deviation.