Lecture 02. Graphical Displays Part 1

7/28/2019 Lecture 02. Graphical Displays Part 1

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Statistics

ST 361

Statistics for Engineers

Graphical Displays

Kimberly Weems

[email protected]

5260 SAS Hall
mailto:[email protected]:[email protected]


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Scales of Measure

Nominal DataPlaces data in categories

Another name for that group

From the article: Do you believe thatextraterrestrial beings have visited Earth at some

time in the past (Believe, Dont Believe, Not sure)

People are in one of three categories.


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Scales of Measure

Ordinal DataCategories that have an order

From the article:How superstitious are you?

(Very, Somewhat, Not very, not at all)

We know that Very is more than Somewhat which

is more than Not very, etc


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Scales of Measure

Note: Numbers can be assigned to thecategories but using the numbers does not

make much sense.

Code: 4 = Very, 3 = Somewhat, 2= Not very, 1=Not at all

Very is not twice as much as Not very.


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Scales of Measure

Interval/RatioNumbers are actually numbers=> make sense as

numbers and can be used that way

From the article: What is your age in years?

Someone who is 40 is twice as old as someone

who is 20. Difference in Age between someone 30

and 35 is the same as the difference between 25

and 30.


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Scales of Measure

Note: Your text refers to this as interval data,some other texts refer to it as ratio data. For

the purposes of this course we will not

differentiate the two.

No real difference between methods of analysis.


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Other terminology:

Categorical data- nominal and ordinal, givesnames to categories.

Numeric data-uses meaningful numbers

Quantitative- another name for numeric Qualitative-another name for categorical


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Example: Intro Stat Students

gender height textbooks HSGPA car

female 69.5 320 3.1 yes

female 65 250 4 no

female 63 150 4 yes

female 64 300 3.35 yes



female 60 250 3 yes


male 72 187 3.1 yes

female 66 150 3.4 no


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female 69.5 320 3.1 yes

female 65 250 4 no

female 63 150 4 yes




female 60 250 3 yes


male 72 187 3.1 yes



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female 69.5 320 3.1 yes

female 65 250 4 no

female 63 150 4 yes




female 60 250 3 yes


male 72 187 3.1 yes



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Why do we care?

Type of data dictates summary that will beused. We must choose the analysis that will be

used.

Summaries of categorical data.Proportions and counts

Example: Superstitious? 2% very, 22%

somewhat, 31% not very, 45% not at all.


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Why do we care?

Summaries of numeric data.Averages, medians, standard deviations

Example: Age? Average 35 years


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Graphics

Statistical Results are often presented ingraphical displays

1 picture = ____________


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Graphics

Statistical Results are often presented ingraphical displays

1 picture = 1000 words

Help understand the story behind the data.

Visualize the distribution

Th th l f d t l i t


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The three rules of data analysis wont

be difficult to remember

1. Make a picturereveals aspects not obvious in the rawdata; enables you to thinkclearly about the patterns andrelationships that may be hiding in your data.

2. Make a pictureto show important features of and

patterns in the data. You may also see things that you did notexpect: the extraordinary (possibly wrong) data values orunexpected patterns

3. Make a picturethe best way to tell others about yourdata is with a well-chosen picture.


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Graphics

Bar Charts- graphical representation ofcategorical data

Horizontal Axis- categories

Vertical Axis- count or percentage of subjects inthat category.

Pie Charts- Angle represents proportion of

values


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Categorical data


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Categorical data

Story: More females than males


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What about numeric values?

Plot numeric values to see where they arelocated.

Stem and Leaf Displays

Dot plot- graphic of numeric data.


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Stem and Leaf Displays

Partition each no. in data into a stem and leaf

Constructing stem and leaf display

1) deter. stem and leaf partition (5-20 stems)

2) write stems in column with smallest stem at top;

include all stems in range of data

3) only 1 digit in leaves; drop digits or round off

4) record leaf for each no. in corresponding stem row;

ordering the leaves in each row helps


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Example: employee ages at a small company

18 21 22 19 32 33 40 41 56 57 64 28 29 29 38 39;

stem: 10s digit; leaf: 1s digit 18: stem=1; leaf=8; 18 = 1 | 8

stem leaf

1 8 92 1 2 8 9 9

3 2 3 8 9

4 0 1

5 6 7

6 4


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Suppose a 95 yr. old is hiredstem leaf

1 8 92 1 2 8 9 9

3 2 3 8 9

4 0 1

5 6 7

6 4

7

8

9 5


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Advantages/Disadvantages of Stem-and-

Leaf Displays

Advantages

1) each measurement displayed

2) ascending order in each stem row

3) relatively simple (data set not too large)

Disadvantages

display becomes unwieldy for large data sets


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Dot Plot

A health researcher examined the amount ofsoda that a group of teenagers consumed

during a day. The resulting amounts in ounces

were: 9, 9, 6, 15, 12, 14, and 40.

0 10 20 30 40


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Dot Plot



were: 9, 9, 6, 15, 12, 14, and 40.

0 10 20 30 40


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Dot Plot



were: 9, 9, 6, 15, 12, 14, and 40.

0 10 20 30 40


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Dot Plot



were: 9, 9, 6, 15, 12, 14, and 40.

0 10 20 30 40


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Dot Plot



were: 9, 9, 6, 15, 12, 14, and 40.

0 10 20 30 40


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Dot Plot



were: 9, 9, 6, 15, 12, 14, and 40.

0 10 20 30 40


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Dot Plot

We can see the main cluster is around 10. Smallest at 6, largest at 40.

Big gap between 40 and the other values.


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Dot Plot

Good for small numbers of values, butbecomes cumbersome with many values.

For larger numbers of values we could stack up

values in categories.


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Histograms

Histogram-bar chart of quantitative dataRange of possible values are broken into

categories

Example: Undergraduate university students

survey: How much did you spend on

textbooks this academic term?

Categories: $0 to $100, $101 to $200, etc.


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Textbooks


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Textbooks

About 20people paidbetween $601and $700


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Textbooks

Amounts centered around $400 More people around $400 than around $200

Values as big as 800 as low as 0.

Useful for understanding the distribution ofquantitative variables.

Where are the main chunks of data?

How spread out are the values?What is the shape of the data?


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TV Time


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TV Time

About 110 peoplespent between 11and 15


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TV Time

Main cluster between 0 and 10 Smallest value 0 and largest value around 60

Cant be below 0, minimum possible. Many

people around the lower limit. Max possible 168. No one around there or

even close.

Values tail off to the right side.


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Shapes of distributions

Skewed to the right (or positively skewed)Long tail to the right

Generally because individuals are stacked up near

a lower limit and unlimited on the upper end.


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Skewed to the left (or negatively skewed)Long tail to the left

Generally because individuals are stacked up near

an upper limit and unlimited on the lower end.


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Birth Year


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Birth Year Traditionalstudents


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Switchedmajors, fiveor six year

students


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students

Nontraditional

students


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students

Nontraditional

studentsOlderstudentsback to for

life change


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SymmetricTails approximately equal in both directions

Major cluster near far from limits on both ends.


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Textbooks

Approximatelysymmetric


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Bimodal


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Bimodal

Peak 1


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Bimodal

Peak 2

Peak 1


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Bimodal-two peaksCaused by two or more groups

Multi-modalseveral peaks

h f di ib i


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Help us understand the dataSkewed=> typically because of a natural limit that

subjects are near

Symmetric => Subjects are not near the limit.

Multi-modal=> multiple distinct groups within the

distribution.


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O li


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Outliers

Recall dot plot40 might be considered an outlier.

Maybe data entry error.

May be actual value.

0 10 20 30 40

Cl P bl


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Class Problem

The following 10 observations on Octobersnow cover for Eurasia during the years 1970-

1979 (in million km2):

Create a stem & leaf display of the data.

Is their an outlier in the data set?

6.5 12.0 14.9 10.0 10.7

7.9 21.9 12.5 14.5 9.2

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Lecture 02. Graphical Displays Part 1