Unit 1: Representing Data & Analysing 2D Data

1.1 Visual Displays of Data

Visual Displays of Data• Use the appropriate display for particular

dataTypes of Data

Quantitative (numerical)

Qualitative (categorical)

Discrete Continuous

Ordinal Nominal

Types of Variables

• Qualitative– Cannot be measured numerically– Ex: eye colour, opinion

–height, distance, mass, time, age, number of moles

•Quantitative/Numerical–can be measured numerically–Ex:

Types of Quantitative Variables

• Discrete– Can be described with whole numbers

– Ex: number of students, pairs of shoes, number of absences

heights of students, length of time a plant takes to germinate

•Continuous–There is a continuum of possible values–Ex:

Name that Data Type

• Age

• Favourite meal

• Television viewing preference

• Volume of radio

• Seating capacity

Quantitative discrete (could be continuous)

Qualitative

Qualitative

Quantitative continuous

Quantitative discrete

Types of Qualitative Data

• Also called categorical• Data can be grouped by specific categories• Ordinal: naturally ordered

– E.g. height (short, average, tall), opinion (poor, satisfactory, good, excellent)

• Interval: each category represents equal amount of time

• Nominal: no natural order– E.g. hair colour, subject

Bar Charts

• Most effective when you wish to emphasize individual items

• Can be used with ordinal or nominal data

0102030405060708090

Num

ber

sold

1stQtr

2ndQtr

3rdQtr

4thQtr

Quarterly Sales

Pie Charts

• Shows frequency distribution

• Can be used for qualitative or quantitative data

• Needs a legend and scale

Quarterly Sales13%

17%

57%

13%

1st Qtr2nd Qtr3rd Qtr4th Qtr

Line Graphs• Suggests trends and

patterns• Change implied as you

move from one item to next

• Should only be used to link data points along interval scale

• Time most common interval

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100

1st

Qtr

2nd

Qtr

3rd

Qtr

4th

Qtr

EastNorth

Additional Graphs

• Stem-and-leaf plot– Good for seeing frequencies of individual items– Measures of central tendency

• Pictograph– Shows frequency distributions– All pictures should be the same size– Needs legend (e.g. = 1 club)

All Graphs Need

• Title

• Labelled axes

• Scale– Qualitative: Nominal categorical, interval

categorical, ordinal categorical

• Legend (pie chart, pictograph)

Identifying Numerical And Categorical Scales

 Average Mark by Reporting Period

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100

Report 1 Report 2 Report 3 Report 4

Mar

k

Grade 9

Grade 10

Grade 11

Grade 12

Identify the categorical scale and the numerical scale.

Mathematically, does it make sense to connect the data points by a line? Why or why not?

How much useful information would be provided if either the categorical or numerical scale where missing?

Numerical

Categorical

Not much! We can’t really tell anything about the graph.Yes: trend lines, and each grade represents an equal interval of time

Classifying Categorical Scales

Sales by Region Graph #2

$0

$20,000

$40,000

$60,000

$80,000

$100,000

North South East West

Sales by Region Graph #1

$0

$20,000

$40,000

$60,000

$80,000

$100,000

North South East West

Nominal Categorical Scale

Line graph inappropriate

Bar graph appropriate

Classifying Categorical Scales

Sales by Quarter Graph #3

$0

$100,000

$200,000

$300,000

$400,000

1stQuarter

2ndQuarter

3rdQuarter

4thQuarter

Qu

art

erl

y S

ale

s

Sales by Quarter Graph #4

$0

$50,000

$100,000

$150,000

$200,000

$250,000

$300,000

$350,000

$400,000

1st Quarter 2nd Quarter3rd Quarter 4th Quarter

Interval Categorical Scale

Line graph appropriate

Bar graph appropriate

Classifying Categorical Scales Average Mark by Grade Graph #5

0

20

40

60

80

100

Grade 9 Grade 10 Grade 11 Grade 12

Average Mark by Grade Graph #6

0

20

40

60

80

100

Grade 9 Grade 10 Grade 11 Grade 12

Interval Categorical Scale (each grade represents an equal amount of time)

Line graph appropriate

Bar graph appropriate

With interval scales, you may use line

graphs or bar graphs – it depends on what

you want to emphasize

Classifying Categorical Scales

Willingness to Wait Graph #7

0

5

10

1st 2nd 3rd 4th

Position in Line

Wai

tin

g T

ime

(min

ute

s)

Willingness to Wait Graph #8

0

5

10

1st 2nd 3rd 4th

Position in Line

Wai

ting

Tim

e (m

inut

es)

Ordinal Scale

Line graph inappropriate

Bar graph appropriate

Split-Bar Graphs

• Used to compare information in which two or more different quantities are represented by the length of the bars

• Who sold more, East or West?

• Who had the best quarter, relative to their total sales?

Quarterly Sales

010203040506070

1stQtr

2ndQtr

3rdQtr

4thQtr

Num

ber

Sold

East West

Quarterly Sales

010203040506070

1stQtr

2ndQtr

3rdQtr

4thQtr

Num

ber

Sold

East West

East: 20 + 25 + 40 + 20 = 105

West:(50-20) + (65-25) + (55-40)

+ (51-20) = 116

Therefore, West sold more, in terms of raw numbers.

Percentage-wise:

East: 40 = 38%____105

West: 40 = 34%____116

Therefore, East had the relatively best quarter.