Organizing and Presenting Data GTECH 201 Session 11

Terminology Classes Frequency Frequency Distribution Categories for grouping data Frequency Number of observations that fall in a class (frequency is a count) Frequency Distribution A listing of all classes along with their frequencies Relative Frequency The ratio of the frequency of a class to the total number of observations Relative Frequency Distribution A listing of all classes along with their relative frequencies Width/Class Interval The difference between the upper and lower cut points (breaks) of a class

Organizing Data Classification Rules Aim is to create categories or classes First step is to compute range Range = Largest Value – Smallest Value Interval or Ratio Scale data only Class Intervals Width of Class Interval Equal based on range Unequal based on range Quantile (Quartile or Quintile) Natural

Classification Methods Natural breaks Equal interval Quantile Manual

How to Decide (on a classification scheme) Rule of thumb: 3 - 7 classes Classification histogram (see later today)

Classification method How many classes to have How to Decide, part II Classification method When to use How many classes to have Natural breaks When attributes are distributed unevenly across the overall range of values Look for natural groups Equal interval When you want all classes to have the same range Easily understood interval, such as 2, 50, 1000, etc. Quantile When attributes are distributed in a linear fashion Determined by purpose of the map Manual When you want classes to break at specific values

Graphs Line graph Bar graph Scatterplots

Creating a Line Graph The growth of the population of students at a Midwestern university is as follows

Line Graph

Bar Graphs Here are data on the percent of females among people earning doctoral degrees in 1990, in several different fields of study

Bar Graph

Scatter Plots Graph bi-variate data when both variables are measured in an interval/ratio or ordinal scale Units for one variable are marked on the horizontal axis Independent variable should always go on the horizontal, x axis

Scatterplots Survey of 3368 people asking them to estimate number of calories in common foods.

Example A city planner collected data on the number of school age children in each of 30 families. Construct a grouped data table using classes based on a single value

Computing Frequency There are three ways you can create classes a < but not equal to b b < but not equal to c a – b, c – d, e - f single value grouping

Distributions Histograms Difference between histograms and bar graphs Bars in a histogram are always vertical Base scale is marked off in equal units; there is no base scale in a bar graph Width of bars in a histogram have meaning Bars in a histogram touch each other

Constructing a Histogram Histogram – height of bar equal to frequency of class represented Bar extends from lowest value to highest value of the class

Histogram Chart

Frequency Polygons Similar to a histogram Midpoint of the class is indicated Points connected by straight lines Cumulative frequency polygon, ogive