# Chapter1 - Web4students

## Chapter1. PICTURING DISTRIBUTIONS WITH PLOTS

TOPICS COVERED - Sections shown with numbers as in e-book

Section 1.1 INDIVIDUALS AND VARIABLES (p. 3)

Individuals and Variables

Individuals are the objects described by a set of data. Individuals may be people, but they may also be animals or things.

Example: Freshmen, 6-week-old babies, golden retrievers, fields of corn, cells

A variable is any characteristic of an individual. A variable can take different values for different individuals.

Example: Age, height, blood pressure, ethnicity, leaf length, first language

Two Types of Variables

A variable can be either

 quantitative o Something that can be counted or measured for each individual and then added, subtracted, averaged, etc., across individuals in the population. o Example: How tall you are, your age, your blood cholesterol level, the number of credit cards you own.

categorical o Something that falls into one of several categories. What can be counted is the count or proportion of individuals in each category. o Example: Your blood type (A, B, AB, O), your hair color, your ethnicity, whether you paid income tax last tax year or not.

How do you decide if a variable is categorical or quantitative?

What are the n individuals/units in the sample (of size “n”)?

What is being recorded about those n individuals/units?

Is that a number (  quantitative) or a statement (  categorical)?

Example Survey students in this classroom: What can be recorded? Gender, Age …

- Individuals: Students in MC students in Dr. Cho’s MA116 class

- Variables: Gender – categorical, Age – Quantitative

- Record Data:

Section 1.2 CATEGORICAL VARIABLES: Pie charts and Bar graphs (p. 6)

Ways to chart categorical data

Because the variable is categorical, the data in the graph can be ordered any way we want (alphabetical, by increasing value, by year, by personal preference, etc.).

Bar graphs

Each category is represented by one bar.

The bar’s height shows the count (or sometimes the percentage) for that particular category

Pie charts

Each slice represents a piece of one whole.

The size of a slice depends on what percent of the whole this category represents.

Section 1.3 QUANTITATIVE VARIABLES: Histograms (p. 11)

Ways to chart quantitative data

Histograms and stemplots

These are summary graphs for a single variable. They are very useful to understand the pattern of variability in the data.

Line graphs: time plots

Use when there is a meaningful sequence, like time. The line connecting the points helps emphasize any change over time.

Other graphs to reflect numerical summaries (see chapter 2)

How to create a histogram

It is an iterative process—try and try again.

Classes: The range of values that a variable can take is divided into equal-size intervals

Frequencies: Count the individuals that fall in each class

What bin size should you use?

Not too many bins with either 0 or 1 counts

Not overly summarized that you lose all the information

Not so detailed that it is no longer summary

Example Continued Survey students in this classroom: gender and age

- Display the distribution of Gender by Pie charts or Bar graphs

- Display the distribution of Age by Histograms – classes

Example 1.2 (p.7): Field of Study

– Go to StatsPortal and Demonstrate how to make a pie chart using EXCEL

1. Click on Resources

2. Click on Data Set

3. Select Excel Format

4. Open Example1.2

5. Highlight the distribution and Insert a PIE GRAPH (in Menu Bar)

6. Highlight the distribution again and Insert a BAR GRAPH (in Menu Bar)

Section 1.4 INTERPRETING HISTOGRAMS (p. 15)

- Look for overall pattern and deviations from the pattern

Overall Pattern described by …

Shape - draw a smooth curve connecting each column roughly: o Symmetric – Bell shaped, Mound shaped, Uniform o Skewed to the right o Skewed to the left o Multimodal

Example: Age of all MC students?

Rolling a 1-6 die?

Heights of female students?

Heights of male and female students?

Exercise: Find an example of left-skewed model.

Deviation describe by …

Outlier - observations that lie outside the overall pattern of a distribution.

Example 1.7 (p. 17): Who takes the SAT?

– Go to StatsPortal and Demonstrate how to make a histogram using CrunchIt!

1. Click on Resources

2. Click on CrunchIt!2.0

3. Select Example7 and Select Graphics

4. Select Histogram

5. Select the variable PctSAT and Select Frequency

6. Leave Optional Parameters blank

7. Click OK

* Now fill in the Optional Parameters to obtain the histogram shown in the book

If you want the one on the book, use 5 bins, width of 20, starting at 0

* Right click on graph

Can Copy and Paste in a word document

Section 1.5 QUANTITATIVE VARIABLES: STEM PLOTS (p. 19)

How to make a stemplot:

Separate each observation into a stem (consisting of all but the final (rightmost) digit), and a leaf (remaining final digit).

Stems may have as many digits as needed, but each leaf contains only a single digit.

Write the stems in a vertical column with the smallest value at the top, and draw a vertical line at the right of this column.

Write each leaf in the row to the right of its stem, in increasing order out from the stem.

Example Make a stemplot for

Original data: 9, 9, 22, 32, 33, 39, 39, 42, 49, 52, 58, 70

Solution:

1.

Sort the data

2.

Assign the values to stems and leaves

Stemplots vs. Histograms

Stemplots are quick and dirty histograms that can easily be done by hand, therefore, very convenient for back of the envelope calculations.

However, they are rarely found in scientific or laymen publications.

Section 1.6 TIME PLOTS (p. 23)

Time Plots : Line Plots - shows behavior over time

Time always goes on the horizontal, or x, axis.

The variable of interest goes on the vertical, or y, axis.

*To construct using CrunchIt!, use Line Plot

*To construct using Excel, use a connected scatter-diagram

ASSIGNMENTS for Chapter 1

1.

Solve all odd numbered problems from the book, answers shown on the back of the book

2.

Go to STATS PORTAL

Click on ASSIGNMENTS