Types of variables Discrete VS Continuous Discrete Continuous Analogous to number of things Continuous Analogous to amounts “the number of” VS “the amount of” The number of cigarettes smoked This amount of nicotine consumed

Exercises Specify whether each of the following measurements are discrete or continuous The number of stairs in a building The height of a tree measured as precisely as possible The number of pages in a book The weight of a book

Displaying data using graphs Categorical Data 1. Pie Charts Show percentages Depict relative size of groups

Displaying data using graphs 2. Bar Graphs Show percentages or frequencies in various categories Can depict two variables simultaneously Can represent proportions that do not sum up to 100%

Displaying data using graphs The same data can be displayed in more than one type of graph:

Displaying Data Using Graphs Quantitative Variables 1. Line graphs/time plots Display a series of observations in sequence Time, depth, height Sequence must be continuous Shows change and rate of change Detect trend

Displaying Data Using Graphs Quantitative Variables 2. Histograms Describe the shape of a variable’s distribution Provide idea of Center Spread Outliers Shape

Displaying Data Using Graphs Center Midpoint Most frequently occurring values Spread Variation about the center Highs, lows, range Outliers Values that lie outside of the data range

Displaying Data Using Graphs Shape Symmetric Distribution Left and right sides of a histogram on either side of the center frequency are mirror-images if each other

Displaying Data Using Graphs Shape Skewed Distribution Not symmetrical Skewed to the left (-) Lower values are more spread out than higher values Skewed to the right (+) Higher values are more spread out than lower values

Displaying Data Using Graphs Distribution Shapes and Characteristics Unimodal Distribution When histogram only shows one prominent peak Bimodal Distribution When there are two prominent peaks observed

Displaying Data Using Graphs 3. Stemplots (Stem and leaf diagrams) Shape of values Range Variation Outliers

Describing Distributions with Numbers Distribution Summary – a set of descriptive statistics that summarize its distribution. Central tendency Spread