Good Morning AP Stat! Day #2

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 StatisticsIntroduction & Chapter 1.1Variables, 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.

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 …

… 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 …

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

Good Morning AP Stat! Day #2