Techniques for Summarizing
Quantitative Data
frequency histogram
A sample of 40 female statistics students were
asked how many times they cried in the previous
month.Their replies were as follows:

Stem-Leaf Plot
A natural way to organize (group) quantitative data is with the order property of the real numbers, i.e., arrange the data from least to greatest. For example, the 30 weights: 185, 160, 235, 165, 125, 175, 185, 132, 168, 112, 170, 155, 105, 158, 120, 190, 140, 185, 125, 180, 145, 110, 155 135, 170, 113, 155, 175, 145, 130 are more easily comprehended in order: 105, 110, 112, 113, 120, 125, 125, 130, 132, 135, 140, 145, 145, 155, 155, 155, 158, 160, 165, 168, 170, 170, 175, 175, 180, 185, 185, 185, 190, 235. Note that each weight has been listed as many times as it occurs. This information can be visually presented with a stem and leaf plot. A position has been chosen to break the numbers into a stem and a leaf. The leaf will always be one digit. The stems are listed on the left, and the corresponding leaves (if any) on the right. Visually a stem-and leaf plot looks like a bar chart; the categories are defined by the decimal structure of the numbers. A stem-and leaf plot for the above data is presented below:

...obtained using simplex algorithm is unique or not?
a) What is the difference between a feasible solution, a basic feasible solution, and an optimal solution of a linear programming problem?
b) What is the difference between simplex solution procedure for a `maximization’ and a `minimization’ problem?
c) Using the concept of net contribution, provide an intuitive explanation of why the criterion for optimality for maximization problem is different from that of minimization problems.
Outline the steps involved in the simplex algorithm for solving a linear programming maximization problem. Also define the technical terms used therein.
3. ``Linear programming is one of the most frequently and successfully employed Operations Research techniques to managerial and business decisions.’’ Elucidate this statement with some examples.
…2…
…2…
4. Describe the transporation problem and give its mathematical model. Explain, by taking an illustration, the North-West Corner Rule, the Least Cost Method and the Vogel’s Approximation Method to obtain the initial feasible solution to a transportation problem.
Discuss the various methods of finding initial feasible solution of a transportation problem and state the advantages, disadvantages, and areas of application for them.
5. What is an assignment problem? It is true to say that it is a special case of the transportation problem? Explain. How can you formulate an assignment problem as a standard linear...

...assume that all the relevant input
data are known with certainty. That is, these models
assume that all the information needed for modeling the
decision-making problem environment is available, with
fixed and known values
For example, deciding how many sections of a course to
offer during a semester can be modeled as a deterministic
model since the costs and benefits of offering each section
are known. The most commonly used deterministic
modelingtechnique is Linear Programming
Probabilistic (also called stochastic) models
assume that some input data are not known with
certainty
That is, these models assume that the values of
some important variables will not be known before
decisions are made
For Example this type of model is the decision of
whether to start a new business venture. As we seen
with high variability in the stock market during the
past several years the success of such venture is
unsure.
Quantitative factors are typically identifiable
and measurable, making their inclusion in the
model relatively easy.
In contrast, qualitative factors measure such
things as perceptions, feelings, and opinions.
Although some qualitative factors do have scales
of measures (for example, we can classify
opinions of the President’s performance as good,
fair, or poor), in general, they are difficult to
quantify and measure
Spreadsheet packages are capable of handling many...

...Question1
Quantitativedata are measures of values or counts and are expressed as numbers (www.abs.gov.au). In other words, quantitativedata are data about numeric variables (www.abs.gov.au). Four types of quantitativedata are interval, nominal, ordinal and ratio.
Firstly, interval scales are numeric scales in which we know not only the order, but also the exact differences between the values (www.mymarketresearchmethods.com). Other than that, interval data also sometimes called integer is measured along a scale in which each position is equidistant from one another (www.changingminds.org). For example agree, neutral and disagree.
Next, nominal data is categories of an object that the researchers are measuring (Hazman, n.d.). The scale categories are merely labels and can only give the frequency. Nominal data are items which are differentiated by a simple naming system and the only thing a nominal scale does is to say that items being measured have something in common, although this may not be described (www.changingminds.org). Nominal items also may have numbers assigned to them. For example, male/female labels are categories to assign people (Hazman, n.d.).
After that, ordinal data not only categorizes variables in such a way as to denote differences among various categories, it also rank-orders categories in...

...Introduction | | |AJ DAVIS is a department store chain, which has many credit customers and wants to find out more information about these customers. A sample of 50 credit customers is selected with data collected on the following five variables:
1. LOCATION (Rural, Urban, Suburban)
2. INCOME (in $1,000's – be careful with this)
3. SIZE (Household Size, meaning number of people living in the household)
4. YEARS (the number of years that the customer has lived in the current location)
5. CREDIT BALANCE (the customers current credit card balance on the store's credit card, in $).
|PROJECT PART A: Exploratory Data Analysis | |
• Open the file MATH533 Sept 2013 Project Consumer.xls from the Course Project Data Set folder in Doc Sharing.
• Students MUST download and use the data file currently posted inside DocSharing. This data set changes each session and IS NOT the same used in prior sessions.
• For each of the five variables, process, organize, present and summarize the data. Analyze each variable by itself using graphical and numerical techniques of summarization. Use MINITAB as much as possible, explaining what the printout tells you. You may wish to use some of the following graphs: stem-leaf diagram, frequency/relative frequency table,...

...Centre for Continuing Education
Executive MBA
(OIL & GAS Management)
Batch: _______________________
Semester: _______________________
Name: _______________________
Sap No/Regn No: _______________________
Assignment – 1
For
QuantitativeTechniques for Management Applications
MBCQ -721
University of Petroleum & Energy Studies
Last Date to submit Assignment-1:-15th Sep 2012
SECTION A (TOTAL MARKS 20)
Each question carries equal marks. Attempt all.
1. Point out the assumptions of Linear Programming. Solve the following by using graphical method; Maximize z =- 5y, subject to x +y ≤ 1, 0.5x + 5y ≥ 0, and x ≥ 0, y ≥ 0.
2. Explain the meaning of two person zero sum game. Define saddle point in a game. Clearly explain the rules of dominance for a game.
3. Define Binomial & Poisson Distributions. A problem in QT is given to three students A, B, and C whose chances of solving it are ½, ¾ and ¼ respectively. What is the probability that the problem will be solved if all of them try independently?
4. Explain the difference and relation between a transportation & assignment problem.
SECTION B (TOTAL MARKS 30)
Each question carries Equal marks. Attempt all.
5. a) In a petroleum engineering workshop there are seven machines for drilling, two for turning, three for milling and one for grinding. Four types of brackets are made. Type A is found by work study to require 7 minutes drilling, 3 minutes turning, 2.5 minutes...

...LIBA
Quantitative Assignment - 1
P 12 - Batch: Students Profile
Submitted To:
Prof. P Lakshmanan
Submitted By:
Group
Contents
|S.No. |Title |Page No. |
|1. |Synopsis |3 |
|2. |Objective |3 |
|3. |Process Chart |4 |
|4. |Limitations |4 |
|5. |Quantitative Tools |4 |
|6. |Analysis |5 |
|7. |Conclusion |15 |
1. Synopsis:
This assignment is taken up in order to understand the personnel profile and behavioral pattern of students who undertake the part time PGDM courses in LIBA. Inferences are drawn from...

...control the situation continuously to achieve these objectives
Definitions
Quantitativetechniques are those statistical and programming techniques, which help decision makers solve many problems, especially those concerning business and industry
Quantitativetechniques are those techniques that provide the decision makers with systematic and powerful means of analysis, based onquantitativedata, for achieving predetermined goals
These techniques involve the use of numbers symbols, mathematical expressions, other elements of quantities, and serve as supplements to the judgment and intuitions of the decision makers
Evolution
The utility of quantitativetechniques has been realized long ago and the science of mathematics is probably as old as the human society
The evolution of industrial engineering, scientific methodologies the were prominent earlier in the natural sciences, were found applicable to management functions-planning, organizing and controlling of operations
19th century, Frederick W. Taylor proposed an application of a scientific method to an operations management problem- Productivity. Determined that the variable that was significant was the combined weight of the shovel (move) and its load.
Henry L. Gantt, devised a chart-to schedule production activities...

...Introduction:
Data analysis is an attempt by the researcher to summarize collected data either quantitative or qualitative. Generally, quantitative analysis is simply a way of measuring things but more specifically it can be considered as a systematic approach to investigations. In this approach numerical data is collected or the researcher transforms collected or observed data into numericaldata. It is ideal for finding out when and where, who and what and any relationships and patterns between variables. This is research which involves measuring or counting attributes (i.e. quantities). It can be defined as:
“The numerical representation and manipulation of observations for the purpose of describing and explaining the phenomena that those observations reflect is called quantitative analysis”
Quantitative analysis gives base to quantitative geography and considered as one of important parts of geographical research. As, subject matter of quantitative geography is comprehended by the following key issues:
Collection of empirical data
Analysis of numerical spatial data
Development of spatial methods for measurements, theories and hypothesis
Construction and testing of mathematical models of spatial theory
Concisely, all above mentioned activities develop understanding of spatial processes....