Good Morning AP Stat! Day #2 Did You Know? Get out NTG … NO Writing … just discuss what you wrote for 5 minutes … Hand in NTG … we’ll discuss Discuss 1.1 – 1.6 Some notes on Section 1.1 …

AP Statistics Introduction & Chapter 1 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. Bar graphs are used to compare things between different groups or to track changes over time.

… more definitions: Pie Chart: A circle graph which represents each category percentage by a number of degrees out of 360. Pie charts are best to use when you are trying to compare parts of a whole. They do not show changes over time

One kind of Quantitative Display: 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 …

Frequency vs. Relative Frequency The count of how many data values fall into a certain class constitutes the frequency for this class.

Frequency vs. Relative Frequency Relative frequency requires one step more. Relative frequency is a measure of what proportion or percent of the data values fall into a particular class. .

2 Way Frequency Table Two-way frequency tables are a visual representation of the possible relationships between two sets of categorical data. The categories are labeled at the top and the left side of the table, with the frequency (count) information appearing in the four (or more) interior cells of the table. The "totals" of each row appear at the right, and the "totals" of each column appear at the bottom. 

4 Steps to organize stats problems 1. Plan (Ask a question): formulate a statistical question that can be answered with data. A good deal of time should be given to this step as it is the most important step in the process. 2. Collect (Produce Data): design and implement a plan to collect appropriate data. Data can be collected through numerous methods, such as observations, interviews, questionnaires, databases, samplings or experimentation.

4 Steps to organize stats problems 3. Process (Analyze the Data): organize and summarize the data by graphical or numerical methods. Graph numerical data using histograms, dot plots, and/or box plots, and analyze the strengths and weaknesses. 4. Discuss (Interpret the Results): interpret your finding from the analysis of the data, in the context of the original problem. Give an interpretation of how the data answers your original questions.

… 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?

Another type of Quantitative Display: 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 …

A Variation on the Theme 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 …

Strong association? Correlation does not imply causation. There is a strong association between swimming on a hot day and eating ice cream. Does that mean that swimming causes you to eat ice cream?

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