Data and data representation (lecture 1)

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

Learning outcomes:
apply numerical skills to business and/or engineering problems
present statistical data in 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.

In brief, you will learn how ...:
To appreciate benefit of numerical data 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.

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

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

LECTURE 1
DATA & DATA REPRESENTATION
Temur Makhkamov
Indira Khadjieva
QM Module Leaders
[e-mail]
[e-mail]
Office hours: by appointment
Room IB 205
EXT: 546

Lecture outline
DATA
the meaning and types of data
sources of data
the scales 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.

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

What is data? (2)
Data may be obtained through already existing-sources or through 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

Primary and Secondary data
Primary data – the data that are obtained as 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:__________________________________________

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

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

Components of the tabular data
Element – the entity or item on which 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

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

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

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

Scale of Measurement

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

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

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

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

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

Aggregate data
Aggregate data – the data that has already been processed to 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).

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.

Population and Sample
Population – a collection of all elements of interest in 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.

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

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

Tabular Methods:
Frequency and Relative frequency tables

Graphical Method: Bar graph

Graphical Method: Pie chart

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

Tabular Methods:
Frequency, relative and cumulative frequency table
Range = 23 – 0 = 23; Group width = 23:5 = 4.6 ≈ 5;
Thus, make the group width = 5 for convenience.

Tabular Method:
Stem-and-Leaf diagram

Graphical Method: Histogram
Histogram

Graphical Method
Cumulative frequency

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

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

Quantitative data: Time series
Case 4:
The company XYZ produces three types of 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.

Tabular form

Graphical form
Component bar graph

Graphical form
Multiple bar graph

Graphical Method
Scatter graph

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

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