Full Name Phone # Birthday Parents’ Names Mom Cell/Work # Dad Cell/Work # Parent email: Extracurricular Activities: List the Math Courses you have taken and the grade you received 1st 2nd 3rd 4th

Turn your card over Write something interesting about yourself on the back… something you want us to know….

Displaying Distributions with Graphs AP Statistics Section 1.1 Displaying Distributions with Graphs

Distributions A distribution can be a table or a graph. It tells us all the values a variable can take, and how often it takes those values. Think about how data is “distributed”.

Examples of Distributions Race Proportion White 62.8% African American 28.4% Asian 5.6% Hispanic 3.2%

Let’s start with a little vocab! Individuals: People, animals, or things for which you are collecting data. Variables: The values of data you are collecting (ex. How many miles a person travels in a week). Always be specific.

Categorical vs. Quantitative Variables Categorical variable – records in which category or group an individual belongs Examples: marital status, sex, birth month, Likert scale Quantitative variable – takes numerical values for which arithmetic operations make sense Examples: height, IQ, # of siblings

Categorical or Quantitative? Race Proportion White 62.8% African American 28.4% Asian 5.6% Hispanic 3.2%

Why it’s important to know the difference between categorical and quantitative variables You will receive NO credit (really!) on the AP exam if you construct a graph that isn’t appropriate for that type of data Type of Variable Appropriate Graph Categorical Pie Chart, Bar Graph Quantitative Dotplot, Stemplot, Histogram

Types of Graphs for Categorical Variables Pie Chart Bar Graph Note: The bars should not “touch” each other. Bars are labeled with the category name.

Pie Chart (Categorical) Categories must make up a whole. Percents must add up to 100%. Music preferences in young adults 14 to 19.

Bar Graph (Categorical) Represent a count OR percent. These do not have to be part of a whole or add up to 100%.

Types of Graphs for Quantitative Variables Dotplots—place a dot above each value of the variable for every time it occurs in the data set

Types of Graphs for Quantitative Variables Stemplots – divide the data into “stems” and “leaves.” Leaves include the last digit (you can round if necessary) It is imperative you have a key.

How to interpret graphs Remember SOCS: Spread, outliers, center, shape Spread—stating the smallest and largest values (note: different from the range where you actually subtract the values). We will talk about other measures of spread later. Outliers—values that differ from the overall pattern. Center—the value that separates the observations so that about half take larger values and about half take smaller values (in the past, you may have heard this called median). Shape—symmetric, skewed left, skewed right. We’ll learn more about shape later.

Activity QUIETLY take your pulse for 60 seconds. Write it down on an index card. Do not put your name on the index card. Bring your index card to me.

Finish up the activity Is this data quantitative or categorical? How could we represent this data? Construct an appropriate graph with your group members.

One-Variable Quantitative Data The most common graph is a histogram. It is useful for large data sets. NOTE—histograms are appropriate graphs for one-variable quantitative data!!!

The height of each bar tells how many students fall into that class. Note that the axes are labeled! Bars include the starting value but not the ending value. The bars have equal width!!!

Reading a Histogram There are 3 trees with heights between 60 and 64. How many trees have heights between 70 and 79? From 70 to 80? Each value on the scale of the histogram is the START of the next bar.

Another Example Refer to p. 20 for an example of a histogram that has a “break” in the scale on one of the axes.

Using the TI Calculator to Construct Histograms Follow the instructions on p. 21 to construct a histogram. Enter the data from Example 1.6 on p. 19. Note: Clear Y= screen before beginning.

Using Your Calculator Effectively Know that the Xscl sets the width of each histogram bar. XMin and XMax should be a little smaller and a little bigger than the extremes in your data set. Beware of letting the calculator choose the bar width for you.

Shape Symmetric – the right and left sides of the histogram are approximately mirror images of each other Skewed Left – there is a long tail to the left Skewed Right – there is a long tail to the right

Examples of Shape Skewed left!

Skewed right!

Now what? Constructing the graph is a “minor” step. The most important skill is being able to interpret the histogram. Remember SOCS? Spread Outliers Center Shape

SOCS Spread: from 7 to 22 Outliers: there do not appear to be any outliers. Center: around 15 or 16 Shape: skewed left

Homework Chapter 1 #9, 16, 18, 27, 38