Displaying Distributions with Graphs Section 1.1

There are two ways to display categorical variables Bar Graphs Pie Charts

How to Construct a Bar Graph Label your axes and title your graph Scale your axes Draw a vertical bar above each category name—make sure bars are at equally spaced intervals

Displaying Quantitative Variables Dotplots Label your axes and title your graph Scale your axes Mark a dot above the number on the horizontal axis corresponding to each data value

Displaying Quantitative Variables Stemplots Separate each data observation into a stem (all but the right most number) and leaf (final number) Write stems vertically in increasing order and draw a vertical line to the right of the stems Write the leaves in increasing order to the right of their corresponding stem Title your graph and add a key

Displaying Quantitative Variables Histograms Divide the range of the data into classes of equal width— make sure there is no overlap of your classes Count the number of observations that fall into each class Label and scale your axes and title your graph Draw a bar that represents the count in each class—there is no space between bars

When examining quantitative variables, you want to look for key components Shape Center Spread Outliers

Shape Three types of shape Symmetric—left and right sides of the graph are approximate mirror images of each other Skewed to the right—right side extends out farther than the left Skewed to the left—left side extends out farther than the right

Symmetric

Skewed to the Right

Skewed to the Left

Practice Problems pg. 10 #1.5, 1.6 pg. 16 #1.8 pg. 18 #1.11

Percentile The pth percentile of a distribution is the value such that p percent of the observations fall at or below it For example, if you are said to be in the 65th percentile for height in your age group then you are as tall or taller than 65% of people your age

Ogive Also known as a relative cumulative frequency graph Helps to find information of an individual observation

How to Construct an Ogive Make a frequency table like you do for a histogram Add three more columns: relative frequency, cumulative frequency, and relative cumulative frequency Label and scale your axes and title your graph Plot a point corresponding to the relative cumulative frequency at the left of the next class interval Begin line at 0% and connect the dots

Time Plot Plots each observation against the time at which it was measured Time is always on the horizontal axis Dots may or may not be connected

Practice Problems pg. 34 #1.24, 1.25, 1.27, 1.28, 1.29