MATH 2400 – Chapter 1

VocabularyIndividuals – the objects described by a set of data (doesn’t have to be people)

Variable – any characteristic of an individual

For Example…

Student

Date of BirthMajor GPA

Etc.

Types of Variables

Quantitative – NumericalEx. – Height, GPA

Categorical - Not usually numericalEx. – Gender, Major, Eye Color, Age, Student ID #

Ex. 1SERIALNO PWGTP AGEP JWMNP SCHL GEND WAGP

283 187 66 6 1 24000

283 158 66 9 2 0

323 176 54 10 12 2 11900

346 339 37 10 11 1 6000

346 91 27 10 10 2 30000

370 234 53 10 13 1 83000

SERIALNO An identifying number for the householdPWGTP Weight in PoundsAGEP Age in yearsJWMNP Travel time to work in minutesSCHL Highest level of education (Ex. 9=high school grad, 10=some college

13=bachelor’s degree)GEND Gender, 1=male and 2=femaleWAGP Annual wage and salary income

Ex. 1 continued…SERIALNO PWGTP AGEP JWMNP SCHL GEND WAGP

283 187 66 6 1 24000

283 158 66 9 2 0

323 176 54 10 12 2 11900

346 339 37 10 11 1 6000

346 91 27 10 10 2 30000

370 234 53 10 13 1 83000

The 6th row is a 53-year-old man who weighs 234 pounds, travels 10 minutes to work, has a bachelor’s degree, and earns $83,000 annually.

Each row represents an individual and each column is a variable.

Vocabulary

Distribution – describes a variable and tells us what values it takes and the frequency of the values

Distribution of a categorical variable – lists the categories and gives either the count or the percent of individuals that fall in each category.

Ex. 2 – Distribution of a Cat. Var.

This table describes the enrollment data for colleges and universities in 2008 for 1.8 million students.

Notice that the percents do not add to be 100%. The exact values would add to be 100%, however the data was rounded to the nearest tenth, so the rounded values only come close. This is roundoff error. This doesn’t mean there is a mistake in our work, its just the result of rounding.

Ex. 2 continued…

Sometimes interpreting numerical data can be easier by looking at it graphically. The above is pie chart for the same data. Pie charts are generally used to emphasize the relationship between a category’s relation to the whole.

Ex. 2 continued…A bar graph of the distribution. The height of each bar represents the percent (but doesn’t necessarily have to).

Bar graphs a more flexible than pie charts. Both display the distribution, but a bar graph can also compare any set of quantities that are measured in the same units.

Ex. 2 continued…The same data, but the categories have been put in descending order.

Can be useful to determine which majors appear most often.

Ex. 3A survey of some Americans over the age of 12 were asked “How much of an impact on your life has this device had?”

The results are shown.

Ex. 3 continued…Can this data be organized into a pie chart?

Can this data be organized into a bar graph?

Ex. 3 continued…

Sometimes interpreting numerical data can be easier by looking at it graphically. The above is pie chart for the same data. Pie charts are generally used to emphasize the relationship between a category’s relation to the whole.

Types of Graphs to UseBar graphs and pie charts are used to visualize

categorical data.

Histograms can be used to visualize numerical data.

Ex. 4On a note card, please indicate the following…

1. Height:2. # of siblings:

include yourself, half-siblings & step-siblings are included as well

3. # of critters:dogs, cats, hamsters, birds, snakes (but don’t count mice if they are snake food), etc.

Ex. 4 Continued…A histogram converts numerical data to

categorical data. Specified intervals of equal width must be specified.

What interval should we use for the heights?What interval should we use for # of siblings?What interval should we use for # of critters?

Create the histogram table, then use Excel to create visual charts.

Histograms

In any graph of data, we should look for an overall pattern and for striking deviations from that pattern.

We can describe the overall pattern of a histogram by its shape, center, and spread.

An important kind of deviation is an outlier, which basically falls outside the overall pattern.

Symmetric and Asymmetric Distributions

If a graph is basically the same on the left as it is the right, it is considered to be symmetric.

If a graph extends much farther in either the left or right direction, it is skewed.

Ex. 5

Stemplots

Use the height data gathered earlier to create a stemplot.

Time Plots

Water Level of the Everglades over time.

Another Time Plot

Do you “Get It?”

Do you “Get It?”

HW: Ch. 1 #13-19, 24, 31These problems can be found at dustintench.pbworks.com MATH 2400 Ch1HW.docx until you get your book.