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*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? **

**Ask: **

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