Week 2 slides_15 (FINANCE1)

transcript

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WEEK 2: ORGANIZING AND VISUALIZING DATA

BUSS1020 Quantitative Business Analysis

BUSS1020 2http://visual.ly/nachos-101

http://visual.ly/power-infographics

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LEARNING OBJECTIVES

In this section you will learn: To construct tables and charts to visualize and organise numerical data

To construct tables and charts to visualize and organise categorical data

The principles of properly presenting summarized data and graphs

Text pages 37-107

Focus is on structured data

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AGENDA

Introduction

Categorical Data Organising One Variable Categorical Data Visualising One Variable Categorical Data Organising Two Variable Categorical Data Visualising Two Variable Categorical Data

Numerical Data Organising Numerical Data Visualising One Variable Numerical Data Visualising Two Variable Numerical Data

Principles of Graphical Excellence

DCOVADCOVADCOVADCOVA

DCOVADCOVADCOVA

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Data is organised and visualized so as to

reveal, glean insight from and communicate

the information,

especially the main features and patterns,

that are hidden within it.

First step: find the “story” in the data

Last step: communicate the “story”, well

ORGANISING AND VISUALISING DATA

ORGANIZING CATEGORICAL DATA: TABLES

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Categorical Data

Tallying Data

Summary Table

One Categorical

Variable

Two Categorical Variables

Contingency Table

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SUMMARY TABLE

Banking Preference? PercentATM 16%

Telephone 2%

Drive-through service at branch 17%

In person at branch 41%

Internet 24%

A summary table indicates the frequency, amount, percentage or proportion of items in each of a set of categories

This allows you to see: the relative frequency of each category the differences between the categories

A Survey of 1000 Bank Customers:

Should the bank stop telephone banking?

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FIDELITY INVESTMENTS

Once considered stopping its bill-paying service for customers

The service was losing money and used by very few customers

However, an analysis of their customer database showed that those using this service were among the most loyal and the most profitable customers.

Fidelity retained the service, so as not to lose those customers who contributed enormously to their profit margin.

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Frequency table results for Type: Count = 316

Summary table for Retirement Fund data: “Type”

Type Frequency Percent of Total

Growth 227 71.8

Value 89 28.2

Retirement Funds.xlsx

SUMMARY TABLE

Risk Frequency Percent of Total

Cumulative Percent of

TotalLow 212 67.1 67.1Average 91 28.8 95.9High 13 4.1 100

Frequency table results for Risk: Count = 316

What type and scale is “Risk”?

Why did I add a Cumulative column?

SUMMARY TABLE

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AGENDA

Introduction

Categorical Data Organising One Variable Categorical DataVisualising One Variable Categorical Data Organising Two Variable Categorical Data Visualising Two Variable Categorical Data

DCOVADCOVADCOVA

VISUALIZING CATEGORICAL DATA (1 VAR)

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Categorical Data

Visualizing Data

BarChart

Summary Table For

One Variable

Contingency Table For Two

Variables

Side-By-Side Bar Chart

Pie Chart

ParetoChart

Chap 2, section 3, pg 53

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Banking Preference

0% 5% 10% 15% 20% 25% 30% 35% 40% 45%

Automated or live telephone

Drive-through service at branch

In person at branch

Internet

VISUALIZING CATEGORICAL DATA: THE BAR CHART

Banking Preference?

ATM 16%

In person at branch

Internet 24%

One bar for each category, bar length represents the amount, frequency or percentage of values in that category

Frequency of Risk level

Percentage of Fund TypeRetirement Fund data

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VISUALIZING CATEGORICAL DATA: THE PIE CHART

A shaded circle with one slice for each category. Slice size represents the percentage in each category.

Banking Preference

Automated or livetelephone

Drive-through service atbranch

In person at branch

Internet

Banking Preference? %

ATM 16%

In person at branch 41%

Internet 24%

Chap 2 pg 54

Frequency of Risk level

Percentages of Risk levelRetirement Fund data

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Chap 2, section 3, pg 55VISUALIZING CATEGORICAL DATA:THE PARETO CHARTFor categorical, nominal scale data

Vertical bar chart, categories shown in descending order of frequency

A cumulative polygon is also shown

Separates the “vital few” from the “trivial many”

Not available in STATCRUNCH!

See pg 92 Berenson for Excel instructions

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Chap 2 pg 57

THE PARETO CHART

nt0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

Incomplete ATM transactions

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AGENDA

Introduction

Categorical Data Organising One Variable Categorical Data Visualising One Variable Categorical DataOrganising Two Variable Categorical Data Visualising Two Variable Categorical Data

DCOVADCOVADCOVA

ORGANIZING CATEGORICAL DATA: TABLES

Categorical Data

Tallying Data

Summary Table

One Categorical

Variable

Two Categorical Variables

Contingency Table

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CONTINGENCY TABLE

Can show pattern or relationship between two or more categorical variables

Cross tabulates or tallies jointly the responses of the categorical variables

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Average High Low TotalGrowth 74 10 143 227Value 17 3 69 89Total 91 13 212 316

Contingency table results:Rows: TypeColumns: Risk

Contingency table for Retirement Fund data: “Type” vs “Risk”

Is there a pattern or relationship?If so, what is it?

CONTINGENCY TABLE

Cell format

Count(Row percent)(Column percent)

Average High Low TotalGrowthRow %

Column %

74(32.6%)

(81.32%)

10(4.41%)

(76.92%)

143(63%)

(67.45%)

227(100%)

(71.84%)

Value 17(19.1%)

(18.68%)

3(3.37%)

(23.08%)

69(77.53%)(32.55%)

89(100%)

(28.16%)Total 91

(28.8%)(100%)

13(4.11%)(100%)

212(67.09%)

(100%)

316(100%)(100%)

Contingency table results:Rows: TypeColumns: Risk

Is there a pattern or relationship?

If so, what is it?

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“PIVOT TABLE” CONTINGENCY TABLE FOR BOND DATA

Fund Number Type Assets Fees

Expense Ratio

Return 2009

3-Year Return

5-Year Return Risk

FN-1 Intermediate Government 7268.1No 0.45 6.9 6.9 5.5Below average

FN-2 Intermediate Government 475.1No 0.50 9.8 7.5 6.1Below average

FN-3 Intermediate Government 193.0No 0.71 6.3 7.0 5.6Average

FN-4 Intermediate Government 18603.5No .13 5.4 6.6 5.5Average

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CAN EASILY CONVERT TO AN OVERALL PERCENTAGES TABLE

Intermediate government funds are much morelikely to charge a fee.

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EASILY ADD VARIABLES TO AN EXISTING TABLE

Chap 2-29

Is the pattern of risk the same for all combinations offund type and fee charge?

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AGENDA

Introduction

Categorical Data Organising One Variable Categorical Data Visualising One Variable Categorical Data Organising Two Variable Categorical DataVisualising Two Variable Categorical Data

DCOVADCOVADCOVA

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VISUALIZING CATEGORICAL DATA (2 VAR)

Categorical Data

Visualizing Data

BarChart

Summary Table For One

Variable

Contingency Table For

Two Variables

Side-By-Side Bar Chart

Pie Chart

ParetoChart

Chap 2 Sect 3 pg 57

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VISUALIZING CATEGORICAL DATA:SIDE-BY-SIDE BAR CHARTSThe side by side bar chart represents the

data from a contingency table.

No Errors

Errors

Invoice Size Split Out By Errors & No Errors

Large Medium Small

Invoices with errors are much more likely to be ofmedium size (61.54% vs 30.77% and 7.69%)

NoErrors Errors Total

SmallAmount

50.75% 30.77% 47.50%

MediumAmount

29.85% 61.54% 35.00%

LargeAmount

19.40% 7.69% 17.50%

Total100.0% 100.0% 100.0%

Risk level vs Fund Type

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PIE CHARTS VS BAR CHARTSWhich is best?

When should each be used?

What properties make a “good” or “bad” pie chart and/or bar chart

http://www.perceptualedge.com/examples.php

What issues can you see with this plot?

http://www.perceptualedge.com/example12.php

www.sharebuilder.com

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Is this better? Why?

Good points?

Negatives?

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40http://flowingdata.com/2012/06/15/what-3-d-pie-charts-are-good-for/

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SOME PRINCIPLES OF GRAPHINGMaximise message; minimise noise

Include a title and label axes

Include a reference to the source

Keep things in correct proportions

Visualize This by Nathan Yau

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Over time

Spatially

HOW DO CATEGORY PROPORTIONS CHANGE?

Interactive graphics

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SPATIAL “HEAT” MAPS

http://www.nytimes.com/interactive/2013/10/02/us/uninsured-americans-map.html?_r=0BUSS1020

CATEGORIES OVER TIMEhttp://www.nytimes.com/interactive/2014/08/13/upshot/where-people-in-each-state-were-born.html?abt=0002&abg=0

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SOCRATIVE QUESTION ON THIS PLOT

https://b.socrative.comRoom:9633CA5F

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SOCRATIVE QUESTION ON THIS PLOT

https://b.socrative.comRoom:9633CA5F

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AGENDA

Introduction

Numerical DataOrganising Numerical Data Visualising One Variable Numerical Data Visualising Two Variable Numerical Data

DCOVADCOVADCOVA

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Chap 2 pg 44 - 51

TABLES FOR ORGANIZINGNUMERICAL DATA

Numerical Data

Ordered Array

CumulativeDistributions

FrequencyDistributions

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Chap 2 pg 44ORGANIZING NUMERICAL DATA: ORDERED ARRAY

Age of Surveyed Uni Students

Day Students

16 17 17 18 18 18

19 19 20 20 21 22

22 25 27 32 38 42Night Students

18 18 19 19 20 21

23 28 32 33 41 45

An ordered array is a sequence of data, in rank order, from the smallest to the largest value.

Shows range: i.e. minimum to maximum value

May help identify “outliers”

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Chap 2 pg 45

ORGANIZING NUMERICAL DATA: FREQUENCY DISTRIBUTIONA frequency distribution is a summary table: data are arranged into numerically ordered classes.

An appropriate number of class groupings, a suitable width of a class grouping, and the boundaries of each class grouping need to be chosen.

The number of class groups depends on the number of values in the data. In general, a frequency distribution should have at least 5 but no more than 15 classes.

To determine the width of a class interval, you divide the range (Highest value–Lowest value) of the data by the number of class groupings desired.

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ORGANIZING NUMERICAL DATA: FREQUENCY DISTRIBUTION EXAMPLEExample: The Bureau of Meteorology (BOM) measures the rainfall (in mm.) in July 2013 for 20 Sydney suburbs:

24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27

Organize this rainfall data

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FREQUENCY DISTRIBUTION EXAMPLESort raw data in ascending order:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Find range: 58 - 12 = 46

Select number of classes: 5

Compute class interval (width): 10 (46/5 then round up)

Determine class boundaries (limits): Class 1: 10 - 20 Class 2: 20 - 30 Class 3: 30 - 40 Class 4: 40 - 50 Class 5: 50 - 60

Compute class midpoints: 15, 25, 35, 45, 55

Count observations & assign to classes

ORGANIZING NUMERICAL DATA: FREQUENCY DISTRIBUTION EXAMPLE

Class MidpointsFrequency

10 - 20 15 3 20 - 30 25 6 30 - 40 35 5 40 - 50 45 4 50 - 60 55 2 Total 20

Data in ordered array:

12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

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RELATIVE & PERCENT FREQUENCY DISTRIBUTION EXAMPLE

Class Frequency

10 - 20 3 .15 15 20 - 30 6 .30 30 30 - 40 5 .25 25 40 - 50 4 .20 20 50 - 60 2 .10 10 Total 20 1.00 100

RelativeFrequency

Percentage

12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

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ORGANIZING NUMERICAL DATA: CUMULATIVE FREQUENCY DISTRIBUTION EXAMPLE

10 ≤ X< 20 3 15% 3 15%

20 ≤ X< 30 6 30% 9 45%

30 ≤ X< 40 5 25% 14 70%

40 ≤ X< 50 4 20% 18 90%

50 ≤ X< 60 2 10% 20 100%

Total 20 100 20 100%

Percentage

Cumulative

Percentage

12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Frequency

Cumulative

Frequency

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WHY USE A FREQUENCY DISTRIBUTION?Condenses raw data into a more useful form

Allows a quick visual interpretation of the data

Enables determination of the major characteristics of the data, including where the data are concentrated / clustered

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FREQUENCY DISTRIBUTIONS: SOME TIPSDifferent class boundaries may provide different pictures for the same data (especially for smaller data sets)

Shifts in data concentration may show up when different class boundaries are chosen

As the size of the data set increases, the impact of alterations in the selection of class boundaries is greatly reduced

When comparing two or more data sets with different sample sizes, you should use either a relative frequency or a percentage distribution

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AGENDA

Introduction

Numerical Data Organising Numerical DataVisualising One Variable Numerical Data Visualising Two Variable Numerical Data

DCOVADCOVADCOVA

VISUALIZING NUMERICAL DATA BY USING GRAPHICAL DISPLAYS

Numerical Data

Ordered Array

Stem-and-LeafDisplay Histogram Polygon Ogive

Frequency Distributions and

Cumulative Distributions

(not in this unit)

Bar chart (discrete data)

Boxplot

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HANS ROSLING

Data Visualisation http://www.youtube.com/watch?v=jbkSRLYSojo

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ORGANIZING NUMERICAL DATA: HISTOGRAMA histogram organizes data into groups (bins); bin size reflects the percentage of data points in each group.

Example:

The Bureau of Meteorology (BOM) measures the rainfall (in mm.) in July 2011 for 20 Sydney suburbs:

24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27

Chap 2-62

5 15 25 35 45 55 MoreF

Histogram: July 2011 rainfall

VISUALIZING NUMERICAL DATA: THE HISTOGRAM

Class Frequency

10 - 20 3 .15 15 20 - 30 6 .30 30 30 - 40 5 .25 25 40 - 50 4 .20 20 50 - 60 2 .10 10 Total 20 1.00 100

RelativeFrequency

Percentage

(In a percentage histogram the vertical axis would be defined to show the percentage of observations per class)

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Chap 2-63

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VISUALIZING NUMERICAL DATA: THE HISTOGRAMA vertical bar chart of the data in a frequency distribution is called a histogram.

In a histogram there are no gaps between adjacent bars for continuous data. There may be gaps for discrete data.

The class boundaries (or class midpoints) are shown on the horizontal axis.

The vertical axis is either frequency, relative frequency, or percentage.

The height of the bars represent the frequency, relative frequency, or percentage when considering identical width bins (intervals, class width).

Chap 2-64

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VISUALIZING NUMERICAL DATA: THE POLYGONA percentage polygon is formed by having the midpoint of each class represent the data in that class and then connecting the sequence of midpoints at their respective class percentages.

The cumulative percentage polygon, or ogive, displays the variable of interest along the X axis, and the cumulative percentages along the Y axis.

Useful when there are two or more groups to compare.

Chap 2-65

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Chap 2 pg 63

5 15 25 35 45 55 65

Frequency Polygon: July 2011 rainfall

VISUALIZING NUMERICAL DATA: THE FREQUENCY POLYGON

Class Midpoints of Rainfall

10 - 20 15 3 20 - 30 25 6 30 - 40 35 5 40 - 50 45 4 50 - 60 55 2

FrequencyClass

Midpoint

(In a percentage polygon the vertical axis would be defined to show the percentage of observations per class)

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VISUALIZING NUMERICAL DATA: THE OGIVE (CUMULATIVE % POLYGON)

10 20 30 40 50 60

Ogive: July 2011 rainfall

10 - 20 10 0

20 - 30 20 15

30 - 40 30 45

40 - 50 40 70

50 - 60 50 90

60 - 70 60 100

% lessthan lowerboundary

Lower class

boundary

Lower Class Boundary

The percentage of observations less than each lower class boundary are plot, versus the lower class boundaries.

Chap 2 pg 64

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AGENDA

Introduction

Numerical Data Organising Numerical Data Visualising One Variable Numerical DataVisualising Two Variable Numerical Data

DCOVADCOVADCOVA

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Chap 2 pg 67VISUALIZING TWO NUMERICAL VARIABLES: THE SCATTER PLOTData consisting of paired observations taken from two numerical variables

One variable measured on the vertical axis; other variable measured on the horizontal axis

Scatter plots are used to examine possible relationships between two numerical variables

SCATTER PLOT EXAMPLE

Volume per day

Cost per day

23 125

26 140

29 146

33 160

38 167

42 170

50 188

55 195

60 200

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Cost per Day vs. Production Volume

20 30 40 50 60 70

Volume per Day

CEO compensation vs company stock return

CEO-compensation.txt Ex 2.89, page 72, Berenson.

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Sales vs Newspaper advertising ($000)

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Chap 2 pg 67VISUALIZING TWO NUMERICAL VARIABLES: THE TIME-SERIES PLOTTime-series plots are used to study patterns in the values of a numeric variable over time.

The numeric variable is measured on the vertical axis and the time period is measured on the horizontal axis.

Frequency of observations is often on an issue.

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TIME SERIES PLOT EXAMPLE

Number of Franchises, 1996-2004

1994 1996 1998 2000 2002 2004 2006

Number of

Franchises

1996 43

1997 54

1998 60

1999 73

2000 82

2001 95

2002 107

2003 99

2004 95Here frequency is annual

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DAILY AORD INDEX: 1995-2013

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50001000

Number of days

http://flowingdata.com/2015/07/02/changing-price-of-food-items-and-horizon-graphs/

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http://www.nytimes.com/interactive/2010/05/27/technology/20100527-apple.html?_r=0

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AGENDA

Introduction

DCOVADCOVADCOVA

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Chap 2 pg 76PRINCIPLES OF GRAPHICAL EXCELLENCEEvery graph should:not distort the data (story). not contain too much “chart junk” or “noise”. have all axes properly and clearly labelled. contain an informative title. be the simplest possible that tells the story. contain the source of the data. objectively and clearly convey the message or “story” in the data.

Further: 3D graphs should have a meaningful 3rd dimension. Usually 2D is sufficient.

The scale on the vertical axis should (usually) begin at zero.

Which plot is better?

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GRAPHICAL ERRORS: CHART JUNK, DISTORTION

1960: $1.00

1970: $1.60

1980: $3.10

1990: $3.80

Minimum Wage

Bad Presentation

Minimum Wage in the US

1960 1970 1980 1990

Good Presentation

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GRAPHICAL ERRORS: NO RELATIVE BASIS

HD’s received by students.

Bad Presentation

Y1 Y2 Y3 HO

Y1=First Year, Y2=Second Year, Y3=Third Year, HO=Honours

Source: University of Sydney Business School

Good Presentation

GRAPHICAL ERRORS: COMPRESSING THE VERTICAL AXIS

Good Presentation

Quarterly Sales Quarterly Sales

Bad Presentation

Q1 Q2 Q3 Q4

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SUMMARYIntroduction

Categorical Data Organising One Variable Categorical Data: Summary Tables

Visualising One Variable Categorical Data: Bar Charts, Pie Charts, Pareto Charts

Organising Two Variable Categorical Data Contingency Tables

Visualising Two Variable Categorical Data Side-By-Side Charts, Time Series, Spatial Charts, 3-D Charts

Numerical Data Organising Numerical Data

Ordered Arrays, Frequency Distributions, Cumulative Distributions

Visualising One Variable Numerical Data Histograms, Polygons, Bar Charts, Ogives

Visualising Two Variable Numerical Data Scatter Plots, Time Series

Week 2 slides_15 (FINANCE1)

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