Data and data representation (lecture 1)

Содержание

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Module Aims:

To foster in students confidence to cope with the processing and

Module Aims: To foster in students confidence to cope with the processing
analyzing of quantitative information.
To provide an appreciation of numerical and statistical concepts relevant to the business environment.

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Learning outcomes:

apply numerical skills to business and/or engineering problems
present statistical data in

Learning outcomes: apply numerical skills to business and/or engineering problems present statistical
a variety of formats, including electronic means
apply basic rules of algebra and calculus
using spreadsheets summarize numerical data into averages and deviations and apply them to a variety of business problems.

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In brief, you will learn how ...:

To appreciate benefit of numerical data

In brief, you will learn how ...: To appreciate benefit of numerical
for businesses
To make decisions based on the numerical data
To interpret and represent numerical data in a most appropriate way depending on your aims
To solve statistics and calculus problems using various quantitative methods
Note: You can find out more about module content in module syllabus and 12-week teaching schedule.

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Teaching methods:

1-hour online lecture each week (online)
2-hour tutorial each week (offline)
1-hour workshop

Teaching methods: 1-hour online lecture each week (online) 2-hour tutorial each week
each week (offline)
You will learn the theory and its application

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Assessment methods:

Two assessments (or components):
In-class test (30%+10%).
30% goes to an in-class test

Assessment methods: Two assessments (or components): In-class test (30%+10%). 30% goes to
in Teaching Week 6
10% goes to weekly online mini-quizzes
Final exam (60%) in Final exam week
True/false
Theory description
Problem solving
Open ended questions
Multiple choice

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LECTURE 1
DATA & DATA REPRESENTATION
Temur Makhkamov
Indira Khadjieva
QM Module Leaders
[email protected]
[email protected]
Office hours:

LECTURE 1 DATA & DATA REPRESENTATION Temur Makhkamov Indira Khadjieva QM Module
by appointment
Room IB 205
EXT: 546

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Lecture outline

DATA
the meaning and types of data
sources of data
the scales

Lecture outline DATA the meaning and types of data sources of data
of measurements for data
DATA REPRESENTATION TECHNIQUES AND TOOLS
analyze the quantitative and qualitative data;
display data in the form of table;
display data in the form of graph.

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What is data? (1)
Data –
the facts and figures that are collected, analyzed

What is data? (1) Data – the facts and figures that are
and summarized.
Examples: data about people, countries, employees
nature, universities, number of products sold, costs, prices,
movies, cars, hospitals, registration numbers, tax codes etc

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What is data? (2)

Data may be obtained through already existing-sources or through

What is data? (2) Data may be obtained through already existing-sources or
statistical studies.
1. already existing-source:
Salaries, sales, advertising costs, inventory levels can be disclosed from a company,
2. from a statistical study:
an experiment, a questionnaire, a survey, etc

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Primary and Secondary data

Primary data – the data that are obtained as

Primary and Secondary data Primary data – the data that are obtained
a result of conducting a questionnaire, a survey, an interview, an observation, etc.
Examples:__________________________________________
Secondary data – the data that come from existing sources. Government institutions, healthcare facilities, Internet and others can provide a great deal of information in a ready-to-estimate format.
Examples:__________________________________________

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Questions:

What data is more costly (expensive):
primary or secondary?
What data is

Questions: What data is more costly (expensive): primary or secondary? What data
more reliable (trustworthy):
primary or secondary?

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Statistical data

Q: What are the components of the statistical table?

Statistical data Q: What are the components of the statistical table?

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Components of the tabular data

Element – the entity or item on which

Components of the tabular data Element – the entity or item on
data are collected.
Examples: Westminster College, Yale Univ., etc
Variable – a characteristic of interest for an element.
Examples: Enrollment, type, etc
Observation – a set of measurements collected for a particular element.
Examples: 953, coed, public, $6,140, etc

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Main types of data
Qualitative data provide labels or names for variables. They

Main types of data Qualitative data provide labels or names for variables.
can be nonnumeric descriptions or numeric codes.
Examples: Coed, Public, etc
Quantitative data show an amount of variables. They indicate either “how much” or “how many” of something.
Examples: 953 students, $6,140 for Room & Boarding, etc

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Question:

Consider this room as an element.
Are its variables such as,
Names

Question: Consider this room as an element. Are its variables such as,
of students quantitative or qualitative?
Mode of students quantitative or qualitative?
Number of students quantitative or qualitative?

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Quantitative Data
Discrete data – the data obtained as a result of counting.
Examples:

Quantitative Data Discrete data – the data obtained as a result of
Number of enrolled students: 500, 1000, 2458, etc.
Continuous data – the data that can take any value within a continuum, limited only by the precision of the measurement instrument.
Examples: Length or height of some object: 5 cm, 5.35 cm,

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Scale of Measurement

Scale of Measurement

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SM for Qualitative Data (1)

Nominal scale – a scale of measurement that

SM for Qualitative Data (1) Nominal scale – a scale of measurement
uses name or label to define a characteristic of an element.

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SM for Qualitative Data (2)

Ordinal scale – a scale of measurement that

SM for Qualitative Data (2) Ordinal scale – a scale of measurement
is nominal and allows ranking or ordering the data according to some criteria.

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SM for Quantitative Data (1)

Interval scale – a scale of measurement that

SM for Quantitative Data (1) Interval scale – a scale of measurement
is ordinal and intervals between data can be used to compare variable observations.

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SM for Quantitative Data (2)

Ratio scale – a scale of measurement that

SM for Quantitative Data (2) Ratio scale – a scale of measurement
is interval and allows considering the ratio of two data values.

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Raw data

Raw data – the data that has not been processed (analyzed,

Raw data Raw data – the data that has not been processed
categorized, put in a table) yet.
Example:
Number of students (total 100), who attended 12 lectures: 100, 98, 85, 76, 64, 55, 76, 87, 96, 98, 99 & 100

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Aggregate data

Aggregate data – the data that has already been processed to

Aggregate data Aggregate data – the data that has already been processed
serve one’s goal.
Example:
On four lectures, the attendance of students was lower than 80 and on other eight lectures it was greater or equal to 80.
(the raw data above have been analyzed).

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Cross-section data – data collected at the same point in time or

Cross-section data – data collected at the same point in time or
based on the same period of time.
Example:
Numbers of different models of automobiles produced by GM Uzbekistan in 2020.
Time series data – data that consist of observations collected at regular intervals over time.
Example:
Number of automobiles produced by GM Uzbekistan during the period from 2010 to 2020.

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Population and Sample

Population – a collection of all elements of interest in

Population and Sample Population – a collection of all elements of interest
a particular study.
Sample – a subset of the population
Example:
All University students vs CIFS students
CIFS students vs 3CIFS1 group
Note: Data about a large group of elements are difficult
to collect due to various restrictions,
therefore only a small part of the group is considered.

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Part 2. Data representation
PART II. Data representation tools and techniques

Part 2. Data representation PART II. Data representation tools and techniques

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Section I Qualitative data:

Case 1. Research conducted on 50 individuals’ choice on

Section I Qualitative data: Case 1. Research conducted on 50 individuals’ choice on GM Uzbekistan automobiles.
GM Uzbekistan automobiles.

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Tabular Methods:

Frequency and Relative frequency tables

Tabular Methods: Frequency and Relative frequency tables

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Graphical Method: Bar graph

Graphical Method: Bar graph

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Graphical Method: Pie chart

Graphical Method: Pie chart

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Quantitative data: Discrete

Case 2. The store sold the following numbers of refrigerators

Quantitative data: Discrete Case 2. The store sold the following numbers of
on 30 different days. Analyze and present the data in tabular and graphical forms.

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Tabular Methods:

Frequency, relative and cumulative frequency table
Range = 23 – 0

Tabular Methods: Frequency, relative and cumulative frequency table Range = 23 –
= 23; Group width = 23:5 = 4.6 ≈ 5;
Thus, make the group width = 5 for convenience.

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Tabular Method:

Stem-and-Leaf diagram

Tabular Method: Stem-and-Leaf diagram

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Graphical Method: Histogram

Histogram

Graphical Method: Histogram Histogram

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Graphical Method

Cumulative frequency

Graphical Method Cumulative frequency

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Quantitative data: Time series

Case 3. the following table shows the profit made

Quantitative data: Time series Case 3. the following table shows the profit
by three cotton companies over four years. Display this data graphically

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Quantitative data: Time series

Times series graph (line graph)

Quantitative data: Time series Times series graph (line graph)

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Quantitative data: Time series

Case 4:
The company XYZ produces three types of

Quantitative data: Time series Case 4: The company XYZ produces three types
products (A, B, and C). The total sales of the Product A in 1999, 2000 and 2001 were £40,000, £45,000 and £50,000, of the Product B were £30,000, £40,000 and £50,000 and of the Product C were £50,000, £55,000 and £60,000 respectively. Construct a table for this data and illustrate it with a help of bar chart.

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Tabular form

Tabular form

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Graphical form

Component bar graph

Graphical form Component bar graph

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Graphical form

Multiple bar graph

Graphical form Multiple bar graph

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Graphical Method

Scatter graph

Graphical Method Scatter graph

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Concluding remarks:

Today, you learnt:
The components of statistical table;
The main types of data;
The

Concluding remarks: Today, you learnt: The components of statistical table; The main
scales of measurement of the data
analyze statistical data;
use tabular methods to display data
use graphical methods to display data

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Essential readings (Part 1)
Jon Curwin…, “Quantitative Methods…”, Chapters 1-2
Glyn Burton…, “Quantitative Methods…”,

Essential readings (Part 1) Jon Curwin…, “Quantitative Methods…”, Chapters 1-2 Glyn Burton…,
Chapter 1
Richard Thomas, “Quantitative Methods…”, Chapter 1.1
Mik Wisniewski…, “Foundation Quantitative…”, Chapter 3
Clare Morris, “Quantitative Approaches…”, Chapter 3
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