Chapter 1.1 Displaying Distributions with graphs.

Variables Individuals: objects described by a set of data Variables: any characteristic of an individual Categorical: Place an individual into one of several groups or categories. Quantitative: Takes numerical values for which arithmetic operations such as adding and averaging make sense. Distribution: tells us what values it takes and how often it takes these values.

When planning a statistical study ask: Why? What purpose do the data have? Who? What individuals does the data describe? What? How many variables do the data contain?

Exploratory Data Analysis: Examining data to find it’s key features. Graphs for Categorical Data: Bar Graph Pie Chart Measurement: Description of the instrument being used, is it appropriate? Count or rate something occurs Examples: Tape measure for height, IQ test for intelligence Variation: The difference in results.

Distribution for Quantitative Variables: Stemplots: Stem: largest place value all the data have in common Leaf: place value following the stem Look at the overall pattern and striking deviations Histograms: Breaks the range of data into intervals and displays only the count or percent of the observations that fall into each interval. Always choose intervals of equal width. Describe the overall pattern by shape, center, and spread Look for outliers Modes: Most Unimodal: One mode Symmetric: Equal values on each side of center(does not have to be exact) Skewed: One side is much longer than the other Frequency: The counts of observations Frequency Table: Displays all the frequencies Relative Frequency: The percentage or fractions of the observations that fall in each interval. Should always round to 100%, but sometimes have a roundoff error.

Looking at the data: Find the cause of outliers before dismissing them Time Plots: Time Series: Measurements of a variable taken at regular intervals over time Seasonal Trend: A pattern that repeats itself at known regular intervals of time Trend: A persistent, long-term rise or fall Looking at the data: Find the cause of outliers before dismissing them