and Organizing Presenting Data
GTECH 201 Session 11
Terminology
Classes
Frequency
Categories for grouping data Number of observations that fall in a class (frequency is a count) A listing of all classes along with their frequencies The ratio of the frequency of a class to the total number of observations A listing of all classes along with their relative frequencies The difference between the upper and lower cut points (breaks) of a class
Frequency Distribution
Relative Frequency
Relative Frequency Distribution
Width/Class Interval
Organizing Data
Classification Rules
Aim is to create categories or classes
Interval or Ratio Scale data only
First step is to compute range Range = Largest Value Smallest Value
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
(on a classification scheme)
How to Decide
Rule of thumb: 3 7 classes Classification histogram (see later today)
How to Decide, part II
Classification method Natural breaks When to use When attributes are distributed unevenly across the overall range of values How many classes to have Look for natural groups
Equal interval
When you want all classes Easily understood interval, to have the same such as 2, 50, 1000, range etc. When attributes are distributed in a linear fashion Determined by purpose of the map
Quantile
Manual
When you want classes to break at specific values
Graphs
250 200
Line graph Bar graph
150 100 50 0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52
100.0 80.0
Scatterplots
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
Yea r 1960 1970 1980 1990 2000 Po p ula t io n Gro w t h 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 s field Bio lo g ic a l S ienc es c Ed ua t io n Eng ineering Physic a l S ienc es c Psyc ho lo g y 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 Psychology Sciences
Scatter Plots
Graph bivariate 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 2 0 4 0
3 0 2 00 0 1 2 1 2 0
0 1 2 0 1
3 2 4 1 3
0 1 0 0 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
Num b er o f Freq uency Rela tive Freq uency Child ren 0 1 2 3 4 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 h...