Organizing and Presenting Data

GTECH 201Session 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)

How to Decide, part IIClassification

methodWhen 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

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Graphs

Line graph

Bar graph

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Creating a Line Graph

Year Population Growth1960 15001970 50001980 146701990 189232000 24000

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

Line GraphPopulation Growth

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Bar Graphs

All fields 29.5Biological Sciences 26Eduation 44.2Engineering 3.8Physical Sciences 12.5Psychology 41.7

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

Bar Graph

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Eduation Engineering PhysicalSciences

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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

ScatterplotsCalories in Common Foods

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

Example

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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

Frequency Relative Frequency

0 12 0.4001 6 0.2002 7 0.2333 3 0.1004 2 0.067

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There are three ways you can create classes

a < but not equal to bb < 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 HistogramC lass Intervals Frequency

Relative Frequency

Midpoint

30 -39 3 0.075 3540-49 1 0.025 4550-59 8 0.2 5560-69 10 0.25 6570-79 7 0.175 7580-89 7 0.175 8590-99 4 0.1 95

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Histogram – height of bar equal to frequency of class represented

Bar extends from lowest value to highest value of the class

Histogram Chart

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Frequency Polygons Similar to a histogram

Midpoint of the class is indicated

Points connected by straight lines

Cumulative frequency polygon, ogive

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