BUS 8375 – Assignment 2 – Tabulated Data

TABLE 1

Respondent

Number

Age

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

21

19

23

21

21

20

26

24

26

30

21

19

17

19

35

27

21

27

21

22

21

19

32

19

Exam

Mark

(%)

87

83

85

81

81

67

75

92

78

89

72

81

75

76

80

75

85

79

90

97

90

87

95

68

Source: Course textbook page 298

Essay

Mark

(%)

83

80

86

75

75

68

88

78

92

95

80

65

77

85

83

60

80

75

93

95

82

86

90

57

Gender

Year in

College

IQ

M

M

M

F

F

F

F

F

M

F

F

M

M

F

F

F

M

M

F

M

M

F

M

F

2

1

4

1

3

3

2

4

4

3

1

2

1

1

3

2

3

4

3

3

2

3

2

3

80

100

98

76

82

99

120

115

126

129

86

80

70

99

99

60

89

70

140

165

115

119

120

89

Understanding

Causality and Big

Data: Complexities,

Challenges, and

Tradeoffs

This example shows two interesting concepts:

correlation and causality from statistics, which

play a key role in Data Science and Big Data.

Correlation means that we will see two

readings behave together (e.g. smoking and

cancer) while causality means one is the cause

of the other. The key point is that if there is a

causality, removing the first will change or

remove the second. That is not the case with

correlation.

Correlation does not mean Causation!

Srinath Perera

Mar 30, 2016

â€œDoes smoking causes cancer?â€

We have heard that lot of smokers have lung

cancer. However, can we mathematically tell that

smoking causes cancer?

We can look at cancer patients and check how

many of them are smoking. We can look at

smokers and check will they develop cancer.

Letâ€™s assume that answers come up 100%. That

is, hypothetically, we can see a 1â€“1 relationship

between smokers and cancer.

Ok great, can we claim that smoking causes

cancer? Apparently it is not easy to make that

claim. Letâ€™s assume that there is a gene that

causes cancer and also makes people like to

smoke. If that is the cause, we will see the 1â€“1

relationship between cancer and smoking. In this

scenario, cancer is caused by the gene. That

means there may be an innocent explanation to

1â€“1 relationship we saw between cancer and

smoking.

This difference is critical when deciding how to

react to an observation. If there is causality

between A and B, then A is responsible. We

might decide to punish A in some way or we

might decide to control A. However, correlation

does warrant such actions.

For example, as described in the post The

Blagojevich Upside, the state of Illinois found

that having books at home is highly correlated

with better test scores even if the kids have not

read them. So they decide the distribute books. In

retrospect, we can easily find a common cause.

Having the book in a home could be an indicator

of how studious parents are, which will help with

better scores. Sending books home, however, is

unlikely to change anything.

You see correlation without a causality when

there is a common cause that drives both

readings. This is a common theme of the

discussion. You can find a detailed discussion on

causality from the talk â€œChallenges in Causalityâ€

by Isabelle Guyon.

Can we prove

Causality?

Great, how can I show causality? Casualty is

measured through randomized experiments

(a.k.a. randomized trials or AB tests). A

randomized experiment selects samples and

randomly break them into two groups called the

control and variation. Then we apply the cause

(e.g. send a book home) to variation group and

measure the effects (e.g. test scores). Finally, we

measure the casualty by comparing the effect in

control and variation groups. This is how

medications are tested.

To be precise, if error bars for groups does not

overlap for both the groups, then there is a

causality. Check https://www.optimizely.com/abtesting/ for more details.

differentiate between correlation and

causality.

Following are examples when causality is

needed.

â€¢

â€¢

â€¢

â€¢

â€¢

Before punishing someone

Diagnosing a patient

Measure effectiveness of a new drug

Evaluate the effect of a new policy (e.g. new

Tax)

To change a behavior

Big Data and Causality

Most big data datasets are observational data

collected from the real world. Hence, there is no

control group. Therefore, most of the time all

you can only show and it is very hard to prove

causality.

However, that is not always practical. For

example, if you want to prove that smoking

causes cancer, you need to first select a

population, place them randomly into two

groups, make half of the smoke, and make sure

other half does not smoke. Then wait for like 50

years and compare.

There are two reactions to this problem.

Did you see the catch? it is not good enough to

compare smokers and non-smokers as there may

be a common cause like the gene that cause them

to do so. To prove causality, you need to

randomly pick people and ask some of them to

smoke. Well, that is not ethical. So this

experiment can never be done. Actually, this

argument has been used before, e.g.

https://en.wikipedia.org/wiki/A_Frank_Statement

.

Obviously, there are lots of interesting

knowledge in observational data. If we can find a

way to use them, that will let us use these

techniques in many more applications. We need

to figure out a way to use it and stop

complaining. If current statistics does not know

how to do it, we need to find a way.

This can get funnier. If you want to prove that

greenhouse gasses cause global warming, you

need to find another copy of earth, apply

greenhouse gasses to one, and wait few hundred

years!!

I find this view blind.

To summarize, Casualty, sometime, might be

very hard to prove and you really need to

First, â€œBig data guys does not understand what

they are doing. It is stupid to try to draw

conclusions without randomized experimentâ€.

I find this view lazy.

Second is â€œforget causality! Correlation is

enoughâ€.

Playing ostrich does not make the problem go

away. This kind of crude generalizations make

people do stupid things and can limit the

adoption of Big Data technologies.

We need to find the middle ground!

When do we need

Causality?

The answer depends on what are we going to do

with the data. For example, if we are going to

just recommend a product based on the data,

chances are that correlation is enough. However,

if we are taking a life changing decision or make

a major policy decision, we might need causality.

Let us investigate both types of cases.

Correlation is enough when stakes are low, or

we can later verify our decision. Following are

few examples.

1. When stakes are low (e.g. marketing,

recommendations) â€” when showing an

advertisement or recommending a product to

buy, one has more freedom to make an error.

2. As a starting point for an investigation â€”

correlation is never enough to prove

someone is guilty, however, it can show us

useful places to start digging.

3. Sometimes, it is hard to know what things

are connected, but easy verify the quality

given a choice. For example, if you are

trying to match candidates to a job or decide

good dating pairs, correlation might be

enough. In both these cases, given a pair,

there are good way to verify the fit.

There are other cases where causality is

crucial. Following are few examples.

1. Find a cause for disease

2. Policy decisions (would 15$ minimum

wage be better? would free health care is

better?)

3. When stakes are too high ( Shutting down a

company, passing a verdict in court, sending

a book to each kid in the state)

4. When we are acting on the decision

( firing an employee)

Even, in these cases, correlation might be useful

to find good experiments that you want to run.

You can find factors that are correlated, and

design the experiments to test causality, which

will reduce the number of experiments you need

to do. In the book example, state could have run

an experiment by selecting a population and

sending the book to half of them and looking at

the outcome.

Some cases, you can build your system to

inherently run experiments that let you measure

causality. Google is famous for A/B testing every

small thing, down to the placement of a button

and shade of color. When they roll out a new

feature, they select a population and rollout the

feature for only part of the population and

compare the two.

So in any of the cases, correlation is pretty

useful. However, the key is to make sure that the

decision makers understand the difference when

they act on the results.

Closing Remarks

Causality can be a pretty hard thing to prove.

Since most big data is observational data, often

we can only show the correlation, but not

causality. If we mixed up the two, we can end up

doing stupid things.

Most important thing is having a clear

understanding at the point when we act on the

decisions. Sometime, when stakes are low,

correlation might be enough. On some other

cases, it is best to run an experiment to verify our

claims. Finally, some systems might warrant

building experiments into system itself, letting

you draw strong causality results. Choose wisely!

Source: https://medium.com/making-sense-ofdata/understanding-causality-and-big-datacomplexities-challenges-and-tradeoffsdb6755e8e220

Retrieved: Dec. 19, 2019

BUSINESS RESEARCH AND DATA

ANALYSIS

LECTURE 10

QUANTIFIED DATA ANALYSIS

BUS8375 â€“ 2022

1

TODAYâ€™S AGENDA

â€¢ Lecture: Quantitative Data Analysis â€“ Ch 15 and 16

â€¢ Assignment 2.

â€¢ Next lectures.

â€¢ Quiz 2 next week after the class Lecture

2

QUANTIFIED DATA ANALYSIS

3

OBJECTIVES

â€¢ Demonstrate the ability to get data ready for quantified

analysis.

â€¢ Describe the various processes by which one can get a

feel for the data in the study.

4

COMMENTS ON TEXTBOOK

â€¢ Substantial amount of material is added to chapter 15

and Ch 16. Please make sure that you understand it. If

you donâ€™t, research the material on your own to grasp

how it all works. Lots of GREAT YouTube videos.

â€¢ For some of you, we will revisit the material that you

have covered in your undergraduate studies.

â€¢ The manipulation of the data assumes that you master

Excel, as studied in your other course in the GBM

program. Again, use YouTube videos to complement it.

â€¢ Chapter 14 â€“ The following material is NOT covered:

â€¢ All elements related to the Excelsior Enterprises case and the

associated software used in the chapter (SPSS). You will instead

use Excel.

â€¢ Testing the goodness of measures.

5

CREATE ORDER

OUT OF

CHAOS

6

THE JOY OF

VISUALIZATION

IT IS ALL ABOUT GETTING

THE MESSAGE TO THE OTHER PERSON!

7

COMPILATION OF THE DATA

â€¢ So, you have administered a

questionnaire as part of your

primary research. You now

have the raw data that has to be

formatted, compiled and

displayed properly.

â€¢ Each person will generate

information that will need to be

combined with all the other

respondents.

â€¢ This raw data will need to be

formatted in a manner that

allows the researcher to

understand the meaning and

possibly start to extract

information.

8

CODING OR TRANSFORMATION OF DATA

â€¢ In some instances, the answers might need to be simplified to

convert it in a useable format. Often this will happen for textual

answers describing a status (education level), feelings (happy,

sad, melancholic, angry, etc.). Numbers will be associated to a

word.

â€¢ At times, you will find in the data that some of the answers donâ€™t

make sense or are inconsistent from previous answers. You will

then need to decide if you cancel only the invalid answer or the

whole data for a particular respondent.

9

TABULATING THE DATA

â€¢ The raw data then needs to

be entered into a data

processor which has the

capability to display this

data in various manners

and to process it to extract

relationships.

â€¢ Many softwares exist to that

effect. We will use Excel as

a processor.

â€¢ Here is the data that we will

use in our ICA 7 today.

10

GETTING A FEEL FOR THE DATA FROM

QUESTIONS

Quantifie

d

analysis

A

B

C

D

11

A. MEASURES OF CENTRAL TENDENCY

â€¢ Mode: Most frequent value.

â€¢ Median: The point where

there is an equal number of

samples on each side.

Mean: Average of a

group of numbers: sum

of xâ€™s / n.

â€¢ Experimental data: 3, 4,

4, 5, 6, 8.

â€¢ Population (the whole).

â€¢

â€¢

N

X

â€¢ Sample (the extracts).

â€¢

â€¢

n

x

12

EXAMPLE

â€¢ Individually.

â€¢ Determine the median, the mode and the mean for the

following numbers:

â€¢ 2 4

8

4 6 2 7

8

4

3 8

9

4 3

5

â€¢ Median: _____

â€¢ Mode: _____

â€¢ Mean (arithmetic average): _____

13

B. MEASURE OF DISPERSION

â€¢ What is this

table

telling us?

â€¢ Range?

â€¢ Min.: ___

â€¢ Max.: ___

â€¢ Creation of

intervals.

14

HISTOGRAM

â€¢ Using data on previous page.

â€¢ X axis is for the range of

measurement. Midpoint is used.

â€¢ Y axis for the measurement.

â€¢ An â€œxâ€ is located at the

measurement for each

segment.

â€¢ This allows us to add a line that

traces the measurement at each

midpoint, creating a

distribution curve. We will use

this curve to calculate the

dispersion

x

x

x

x

x

x

x

15

HISTOGRAM TO DISTRIBUTION CURVE

â€¢ Second level of analysis as we try to figure out the â€œspreadâ€

and behaviour of the data. Range: min. to max. range.

â€¢ Graphic representation of sampling an event, activity, etc.

16

MEASURE OF DISPERSION

â€¢ What can you tell me by looking at these 3 super- imposed graphs?

Donâ€™t forget, you are looking at a data distribution pattern here.

â€¢ If for an exam, which class do you want to be in?

17

MEASURES OF SHAPE

â€¢ Compared to a NORMAL distribution, is the data leading

one way or the other way?

â€¢ Skewness = 3(Âµ:mean â€“ Md:median) / Ïƒ:standard

deviation.

â€¢ Higher the number, more skewed is the distribution.

18

MEASURE OF DISPERSION

â€¢ A company builds advanced computers. Daily production

data: 5, 9, 16, 17 and 18. Total production of 65.

â€¢ Average daily output (mean): 13 (i.e. total production / no. of

days).

â€¢ Deviation from the mean (Âµ); how does each daily output

compares with the average (sum is always or near zero):

Deviation = Daily production – Mean

19

VARIANCE AND STANDARD DEVIATION

â€¢ Variance is the average

of the squared

deviations.

â€¢ Standard deviation is the

most popular way of

measuring the spread of

data.

â€¢ PAY ATTENTION!

â€¢ For calculating the std

deviation of a sample

data instead of using N

as a denominator, we

will use n-1. Rest of the

formula is the same i.e.

std Dev of sample = sq

rt( Sum of Sq / n-1)

20

VERY USEFUL TOOL – NORMAL CURVE

â€¢ Â±Ïƒ. Â±2Ïƒ and Â±3Ïƒ: extent of distribution; standard

deviation.

21

NORMAL CURVE â€“ SEEN IS A

DIFFERENT WAY

â€¢ Â±Ïƒ. Â±2Ïƒ and Â±3Ïƒ: extent of distribution; standard

deviation.

22

C. VISUAL SUMMARY â€“ 1 VARIABLE

â€¢ Histogram is a type of

vertical bar that is

used to depict a

frequency distribution.

â€¢ Can depict multiple

years on same graph.

23

VISUAL SUMMARY â€“ 1 VARIABLE

â€¢ Pie chart is a

circular depiction of

data where the area

of the whole pie

represents 100% of

the data and the

slices represent the

breakdown of the

sublevels.

24

D. MEASURE OF RELATION â€“ 2

VARIABLES

â€¢ A scatterplot is a twodimensional graph plot of

pairs of points from two

numerical variables.

â€¢ What are the 2 key

components of this scatter

plot?

â€¢ What would be a pair of

data?

â€¢ What can you deduct by

looking at this graph?

â€¢ Correlation (relationship)

is NOT causation!

25

THE DANGER OF SCATTERPLOTS

â€¢ What is the message in

this graph?

â€¢ Does this graph make

sense?

â€¢ Why?

â€¢ DANGER!

Source: Cairo, A., (2019), Does Obesity Shorten Life?

Scientific American, (321), 3, p. 100

26

MEASURE OF CORRELATION

â€¢ How one parameter relates to the other parameter.

â€¢ Correlation, not causation, i.e. not what leads to what.

â€¢ Higher the number, greater the link between the two.

27

CORRELATION – EXAMPLES

â€¢ Many parameters can be analysed in a 2-dimensional aspect. 3

(or more)-dimensional is also possible but becomes more

challenging (AI for optimum solution).

28

CORRELATION AND CAUSATION

â€¢ Easily confusing.

â€¢ Should ice cream be banned

in the summer?

â€¢ Is there something wrong

with this graph?

â€¢ What conclusion can we

generate from this

information?

â€¢ What is the causation of the

number of drowning?

â€¢ DANGER, DANGER!

â€¢ Correlation is generally

symmetrical, Causation is

directional.

29

CAUSATION

â€¢ At times, easy to see. You want to

move an object? You push it. That is

causation.

â€¢ The direct relationship, called

dependency, has to be proven

through a series of experiments.

â€¢ This dependency can be multidimensional, i.e. more than over

variable. E.g. increase is sales can

be caused by more than price

reduction.

â€¢ READ excellent article loaded on

eConestoga.

30

RAW DATA – 1

31

RAW DATA – 2

32

ASSIGNMENT 2

â€¢ Raw data is only a mean to understand a variable.

â€¢ To understand we need to convert this raw data into useable

information.

â€¢ Then we need to integrate this data into a format that is user

friendly.

â€¢ A variety of tools are available that will allow us to let the

data â€œtalkâ€ to us.

â€¢ You must master Excel.

â€¢ Assignment 2 has master data file. Use this file to answer 4

questions listed in the second file for assignment 2. Show the

details for your work. Submit answer for each question in its

corresponding worksheet in the Excel file

33

KEY WORDS AND CONCEPTS

â€¢ Raw data

â€¢ Coding

â€¢ Tabulation

â€¢ Data processor

â€¢ Population

â€¢ Sample

â€¢ Central tendency

â€¢ Median

â€¢ Mode

â€¢ Mean

â€¢ Range

Histogram

Pie chart

Distribution curve

Normal curve

Variation

Standard deviation

Measure of

dispersion

â€¢ Scatterplot

â€¢ Correlation

â€¢ Causation

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

â€¢

34

WRAP-UP OF LECTURE

â€¢ Raw data is only a mean to understand a variable.

â€¢ To understand we need to convert this raw data into

useable information.

â€¢ Then we need to integrate this data into a format that is

user friendly.

â€¢ A variety of tools are available that will allow us to let

the data â€œtalkâ€ to us.

â€¢ You must master Excel.

35

NEXT SESSION

â€¢ Week 11 â€“ Lec. 10:

â€¢ Lecture: Qualitative Analysis â€“ Ch 17

â€¢ Quiz 2.

â€¢ Final Exam Review

36

BUSINESS RESEARCH AND DATA

ANALYSIS

LECTURE 11

QUALIFIED ANALYSIS

BUS8375 â€“ 2022

1

TODAYâ€™S AGENDA

â€¢ Lecture: Qualified Analysis, Chapter 17.

â€¢ Quiz 2 is after Lecture today

â€¢ Group Project report submission was due before start of

Lecture today

2

LECTURE

QUALITATIVE ANALYSIS

CH 17

3

OBJECTIVES

â€¢ Discuss the 3 important steps in qualitative analysis:

â€¢ Data reduction

â€¢ Data display

â€¢ Drawing conclusions.

â€¢ Discuss reliability and validity.

4

COMMENTS ON TEXTBOOK

â€¢ Chapter 17, with the exception of:

â€¢ Some other methods of gathering and analyzing qualitative data

â€¢ Big Data.

5

CREATE ORDER

OUT OF

CHAOS

6

CHAOS

â€¢ After proceeding with a series of interviews, observations

and questionnaires (i.e. with open ended questions),

researchers end up with a large quantity of text; RAW DATA

(i.e. chaos).

â€¢ This valuable data (assuming that the process and the

questions used were appropriate (so many concerns here)),

needs to be compiled in a manner that will allow the

researcher to extract the messages that are communicated

by the respondents.

â€¢ This is MOST CHALLENGING, particularly compared to

quantified analysis that allows a variety of mathematical

tools to process the raw data that is numerical.

â€¢ One tool is recognized as the bench mark in this analysis:

1. Data reduction

2. Data display

3. Drawing conclusions.

7

1. DATA REDUCTION â€“ 1

â€¢ The ultimate goal is to get the data to â€œTalk to usâ€.

â€¢ The raw data is overwhelming and needs to be reduced

in segments that can be managed individually, then

categorized.

â€¢ This process is NOT LINEAR (i.e. continuous) but

ITERATIVE (i.e. back and forth), because adjustments will

be needed as progress is made.

â€¢ FIRST STEP: the raw data needs to be rearranged into

groups through a coding process. Coding will take

recurring themes and provide titles under which these

ideas will be grouped. These are also called

CATEGORIES.

â€¢ This process might require the re-reading of the raw data

a few times (i.e. iteration) to see patterns and

connections emerge between the various statements that

were compiled in the raw data.

8

1. DATA REDUCTION â€“ 2

â€¢ Coding units (also called categories) are selected; words

(2 to 10 max.) that describe the various components of

what is in the raw data.

â€¢ This will create a list of code and categories that will be

used to analyze the raw data.

â€¢ The coding will be done for 2 types of information:

â€¢ Categories that are being studied, e.g. theme, issue, idea (rows)

â€¢ Categories of answers for each category being studied (column)

â€¢ The goal is to identify recurring topics, comments,

suggestions, etc. that can be combined through

similarities.

â€¢ From the mass of collected data, the researcher has to

identify common threads.

â€¢ The challenge will be to decide what data is NOT USED

as there are one-off comments that are â€œoutliersâ€, which

cannot be used. These are discarded as not meaningful.9

1. DATA REDUCTION â€“ 3

â€¢ At times you might want to quantify the frequency of a

category that is being mentioned in the raw data. This can

be applied to both rows and columns.

â€¢ The categorisation of columns, can vary from row to row

depending on the questions asked and the answers found

in the raw data. This will provide flexibility in the analysis

of the parameters measured, i.e. the rows.

â€¢ Often a column is added where comments can be

inserted for the categories in the rows.

â€¢ Finally, in each cell at the intersections of rows and

columns, information is provided that either quantifies the

intersection (i.e. the frequency of the intersection) or

describes the meaning of the intersection.

10

2. DATA DISPLAY â€“ 1

â€¢ The display that will be created by the researcher will vary

from project to project. The design of the display will need to

adapt to the coding/category that was created by the

researcher through its questions, structure and survey

design.

â€¢ The display will generally be a spreadsheet with one axis

listing a series of parameters (areas studied â€“ variables)

with the other axis listing another series of parameters

(feedback received on each variable).

â€¢ The goal is to establish relationships between these 2

parameters , generating a series of â€œmessagesâ€ from which

the researchers will be able to generate observations,

possibly leading to recommendations.

â€¢ The number of categories in each axis will also depend on

the situation that is being analysed.

11

â€¢ 3 components: Rows, Columns and Cells.

2. DATA DISPLAY â€“ 2

â€¢ Once the number of rows (areas studied) and columns

(comments in the raw data that are related to the areas

studied (i.e. each row)) are determined, the spreadsheet

is created.

â€¢ Quantification can be used to measure the frequency that

each category is mentioned. This can be applied to the

rows (area studied) or to individual cells. This will begin

the interpretation of the data.

â€¢ Often, a column of comments is added, allowing the

researcher to insert comments for rows (areas that are

studied) allowing the identification of a particular point

(e.g. pattern and relationship) that is worth mentioning.

â€¢ In addition to a spreadsheet, other methods can be used:

networks or diagrams that will allow the researcher to

12

present relationships between concepts in the data.

3. DRAWING CONCLUSIONS

â€¢ After a few iterations, the researcher will be able to better

understand the information gathered, i.e. the answers or

the feedback provided.

â€¢ The iterative process is key in understanding the data as

it forces a reflection not only on the content, but on the

relationships (i.e. the structure) in the data.

â€¢ The interpretation of the data will lead the researcher to

draw conclusions from this data.

â€¢ At the same time, the researcher has to take the feedback

provided (i.e. conclusion) and relate it to what is

â€œpossibleâ€ as other parameters might constraint

(availability of resources ($, people or time),

rules/laws/ethic, relevancy, etc.) the implementation of

the findings.

13

RELIABILITY AND VALIDITY

â€¢ Key points need to be considered in regard to the quality of

the data:

â€¢ The quality of the survey (I-O-Q); questionnaire and sampling

design

â€¢ The â€œhonestyâ€ of the respondents; any misunderstanding of the

questions or the presence of bias in the answers

â€¢ The â€œhonestyâ€ of the researcher in structuring and compiling the

data.

â€¢ Category reliability (for both rows and columns) will be

affected by the above points, as these points might impact

the selection of the categories used.

â€¢ One approach to increasing reliability and validity is to

have various people involved at each stage, checking the

work done in the previous stage. Also, the raw data can be

analysed (creation of the spreadsheet ) individually by 2 or

3 people, then compared to see the similarities or

differences.

14

KEY WORDS AND CONCEPTS

â€¢ Qualitative data

â€¢ Category reliability

â€¢ Data reduction

â€¢ Data display

â€¢ Data coding

â€¢ Reliability

â€¢ Validity

â€¢ Continuous process

â€¢ Iterative process

â€¢ Patterns

â€¢ Connections

â€¢ Outliers

15

WRAP-UP OF LECTURE

â€¢ Textual answers provide an opportunity for researchers to

gather â€œopenâ€ answers that might not be captured in a

quantified analysis (closed-ended questions).

â€¢ The raw data gathered can be substantial and complex to

distill.

â€¢ This data need to be simplified, then compiled within a

structure (often a spreadsheet) in order to provide

categories from which it will be possible through the

interpretation of the structured data to identify patters and

relationships.

â€¢ A high reliability and validity is more challenging to achieve

than for quantified data analysis.

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NEXT SESSION

â€¢ Lecture 12: Course Overview of processes and tools.

â€¢ Discussion on Final Exam.

â€¢ Wrap-up of course.

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