AP Statistics Introduction & Chapter 1.1 Variables, Distributions & Graphs Goals: What will we know and be able to do as a result of today’s Lesson?

You will be able to know, explain and use the following vocabulary: Individual Variable Categorical Variable Quantitative Variable Distribution Exploratory Data Analysis Count Percent Bar Graph Pie Chart Dotplot Stemplot Center, Spread, Shape Outlier

Here are some definitions: Individual : Objects described by a set of data. They may be people, animals, things, etc. Variable : Any characteristic of an individual. The variable will likely take on different values for different individuals. (Can you think of some more examples?)

… more definitions: Categorical Variable : A variable which focuses on a characteristic of an individual, allowing it to be placed into one of several groups or categories. Quantitative Variable : A variable which focuses on a characteristic of an individual that takes on numerical values for which arithmetic operations can be performed. (Can you think of some more examples?)

… more definitions: Distribution : a way of demonstrating what values a variable take on and how often it takes each value. Exploratory Data Analysis : Using statistical tools to examine data and describe its main features. Comparing variables, providing graphs and doing numerical summaries are specific strategies.

… more definitions: Count : The number of observations that fall into a particular category, when analyzing individuals with a categorical variable. Percent : The percentage of observations that fall into a particular category, when analyzing individuals with a categorical variable. This is found by dividing the count by the total number of observations.

… more definitions: Bar Graph : A graph which is fashioned by separate rectangular bars, whose heights represent either the count or the percentage of individuals within each category.

… more definitions: Pie Chart: A circle graph which represents each category percentage by a number of degrees out of 360.

Dotplot: A simple way to represent a summary of quantitative data. Create an x-axis with the quantitative values upon it. Place a dot over each value as it is represented in the data. See the example done in class for soccer goals … One kind of Quantitative Display:

… more definitions: Looking for an overall PATTERN? Center : What value seems to divide the data into two parts - half of which are higher, and half of which are lower? Spread : What are the largest and smallest values? Shape : Do the data form a symmetric mound? … Is the distribution flat? … Does it have a tail? … to the left? … or to the right? Outlier : Do any individual observations fall outside the overall pattern of a graph?

Stemplot: A more complicated way to represent a summary of quantitative data, especially when the spread of the data is very large. Separate each observation in two parts, a stem and a leaf (as demonstrated in class). Write the stems vertically in increasing order. Draw a vertical line to the right of the stems. Go though the data, writing down the leaves to the right of each stem. Rewrite the leaves in increasing order. Provide a key for what each stem/leaf means. See the example done in class for Caffeine content … Another type of Quantitative Display:

Split Stemplot: Allow the 2 stems of the same value to represent an upper and lower half of the leaves. Tips: Make sure you always have the same number of leaves allotted to each stem when splitting stems Five stems is a good minimum Too many stems will flatten the graph Too few will create a “skyscraper” shape You achieve greater flexibility by rounding the data first. See the example done in class for Caffeine content … A Variation on the Theme

What’s on for tomorrow?? The remainder of Section 1.1 – Histograms and your TI-83