Organizing and Presenting Data

GTECH 201 Session 11

Terminology

      Classes  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

Natural breaks Equal interval Quantile Manual

How to Decide, part II

When to use

When attributes are distributed unevenly across the overall range of values When you want all classes to have the same range

How many classes to have

Look for natural groups Easily understood interval, such as 2, 50, 1000, etc.

When attributes are distributed in a linear fashion When you want classes to break at specific values Determined by purpose of the map

 Line graph  Bar graph  Scatterplots

Graphs

250 200 150 100 50 0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 49 41 33 25 17 9 1 100.0

0 50 100 150 200 250 80.0

60.0

40.0

20.0

0.0

0 50 100 150 200 250

Creating a Line Graph

 The growth of the population of students at a Midwestern university is as follows Year 1960 1970 1980 1990 2000 Population Growth 1500 5000 14670 18923 24000

Line Graph

Population Growth 30000 25000 20000 15000 10000 5000 0 1 2 3 4 5 Population Growth

Bar Graphs

 Here are data on the percent of females among people earning doctoral degrees in 1990, in several different fields of study All fields Biological Sciences Eduation Engineering Physical Sciences Psychology 29.5

26 44.2

3.8

12.5

41.7

Bar Graph

50 45 40 35 30 25 20 15 10 5 0 All fields Biological Sciences Eduation Engineering Physical Sciences Psychology

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

Calories in Common Foods

450 400 350 300 250 200 150 100 50 0 -50 0 2 4 6 8 10 12  Survey of 3368 people asking them to estimate number of calories in common foods.

Example

0 3 0 0 3 0 2 2 00 1 2 1 0 0 1 2 4 0 4 2 1 0 1 0 0 2 0 1 3 2

  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

Number of Children 0 1 2 3 4 Frequency Relative Frequency 12 6 7 3 2

30

0.400

0.200

0.233

0.100

0.067

1.000

 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

  Class Intervals Frequency 30 -39 40-49 50-59 60-69 70-79 80-89 90-99 3 1 8 10 7 7 4

40

Relative Frequency 0.075

0.025

0.2

0.25

0.175

0.175

0.1

1

Midpoint 35 45 55 65 75 85 95 Histogram – height of bar equal to frequency of class represented Bar extends from lowest value to highest value of the class

20 15 10 5 0

Histogram Chart

150% 100% 50% 0% Frequency Cumulative %

Frequency Polygons

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

250 200 150 100 50 0 S1