Q1. (a) What is the difference between a qualitative and quantitative variable? [5 Marks] (b) A town has 15 neighbourhoods. If you interviewed everyone living in one particular neighbourhood, would you be interviewing a population or a sample from the town? Would this be a random sample? If you had a list of everyone living in the town, called a frame, and you randomly selected 100 people from all neighbourhoods, would this a random sample? [5 Marks]

Answer:
(a) Qualitative data deals with meanings while quantitative data deals with numbers. Qualitative data describes properties or characteristics that are used to identify things. Quantitative data describes data in terms of quantity using the numerical figure accompanied by measurement unit. Statistics deals only with quantitative data.

Statistics deals with numerical data, which can be expressed in terms of quantitative measurements. So, the qualitative phenomenon like beauty, intelligence cannot be expressed numerically and any statistical analysis cannot be directly applied on these qualitative phenomena. But Statistical techniques may be applied indirectly by first reducing the qualitative data to accurate quantitative terms. For example, the intelligence of a group of students can be studied on the basis of their marks in a particular examination.

i) The number of transactions occurring in an ATM per day -- Quantitative data

ii) The popular brand name in cars is Maruthi. – Qualitative data

If want to do statistic in a particular area and interviewed everyone then it is called as population and if you doing statistic analysis for a town and interviewed only 15 neighborhoods then it is called that interviewing a sample from town. It is also called “chunk” which refers to the fraction of the population being investigated which is selected neither by probability nor by judgment.

Moreover, a list or framework should be available for the selection of the sample. It is used to make pilot...

...LESSON – 1
STATISTICS FOR MANAGEMENT
Session – 1 Duration: 1 hr
Meaning of Statistics
The term statistics mean that the numerical statement as well as statistical methodology. When it is used in the sense of statistical data it refers to quantitative aspects of things and is a numerical description.
Example: Income of family, production of automobile industry, sales of cars etc. These quantities are numerical. But there are some quantities, which are not in themselves numerical but can be made so by counting. The sex of a baby is not a number, but by counting the number of boys, we can associate a numerical description to sex of all newborn babies, for an example, when saying that 60% of all live-born babies are boy. This information then, comes within the realm of statistics.
Definition
The word statistics can be used is two senses, viz, singular and plural. In narrow sense and plural sense, statistics denotes some numerical data (statistical data). In a wide and singular sense statistics refers to the statistical methods. Therefore, these have been grouped under two heads – ‘Statistics as a data” and “Statistics as a methods”.
Statistics as a Data
Some definitions of statistics as a data are
a) Statistics are numerical statement of facts in any...

...Master of Business Administration- MBA Semester 1
MB0040 – Statistics for Management
Assignment Set - 1
Q1. Define “Statistics”. What are the functions of Statistics? Distinguish between Primary data and Secondary data.
Answer: Statistics: Statistics as a discipline is considered indispensable in almost all spheres of human knowledge. There is hardly any branch of study which does not usestatistics. Scientific, social and economic studies use statistics in one form or another. These disciplines make-use of observations, facts and figures, enquiries and experiments etc. using statistics and statistical methods. Statistics studies almost all aspects in an enquiry. It mainly aims at simplifying the complexity of information collected in an enquiry. It presents data in asimplified form as to make them intelligible. It analyses data and facilitates drawal of conclusions.
Important functions of statistics:
Presents facts in simple form: Statistics presents facts and figures in a definite form. That makes the statement logical andconvincing than mere description. It condenses the whole mass of figures into a singlefigure. This makes the problem intelligible.
Reduces the Complexity of data: Statistics simplifies the complexity of data. The raw data are unintelligible. We make themsimple and...

...population with a specific distribution.
The Kolmogorov-Smirnov (K-S) test is based on the empirical distribution function (ECDF). Given N ordereddata points Y1, Y2, ..., YN, the ECDF is defined as
\[ E_{N} = n(i)/N \]
where n(i) is the number of points less than Yi and the Yiare ordered from smallest to largest value. This is a step function that increases by 1/N at the value of each ordered data point.
The graph below is a plot of the empirical distribution function with a normal cumulative distribution function for 100 normal random numbers. The K-S test is based on the maximum distance between these two curves.
Characteristics and Limitations of the K-S TestAn attractive feature of this test is that the distribution of the K-S test statistic itself does not depend on the underlying cumulative distribution function being tested. Another advantage is that it is an exact test (the chi-square goodness-of-fit test depends on an adequate sample size for the approximations to be valid). Despite these advantages, the K-S test has several important limitations:
1. It only applies to continuous distributions.
2. It tends to be more sensitive near the center of the distribution than at the tails.
3. Perhaps the most serious limitation is that the distribution must be fully specified. That is, if location, scale, and shape parameters are estimated from the data, the critical region of the K-S test is no longer valid. It typically must be determined by simulation....

...successful that after World War II many companies used similar techniques in
managerial decision making and planning.
The decision making task of modern management is more demanding and more important
than ever. Many organisations employ operations research or management science personnel or
consultants to apply the principles of scientiﬁc management to problems and decision making.
In this module we focus on a number of useful models and techniques that can be used in the
decision making process. Two important themes run through the study guide: data analysis and
decision making techniques.
Firstly we look at data analysis. This approach starts with data that are manipulated or processed
into information that is valuable to decision making. The processing and manipulation of raw
data into meaningful information are the heart of data analysis. Data analysis includes data
description, data inference, the search for relationships in data and dealing with uncertainty
which in turn includes measuring uncertainty and modelling uncertainty explicitly.
In addition to data analysis, other decision making techniques are discussed. These techniques
include decision analysis, project scheduling and network models.
Chapter 1 illustrates a number of ways to summarise the information in data sets, also known as
descriptive statistics. It includes graphical and tabular summaries, as well as summary measures
such as...

...MBA SEMESTER 1
MB0040 – STATISTICS FOR MANAGEMENT
Assignment
Roll No.
1- Statistical survey is a scientific process of collection and analysis of numerical data used to collect information about units.
Questionnair and schedule are both methods of collecting data in statistical survey. At questionnair the questions is sent by mail to respondents to fill it and send it back. At schedule the questions is filled by the enumerator.
Questionnair is a cheaper process than schedule when it was in a large samples or population. Questionnair should be filled by litrate and cooperative but scheduke is filled enumurator. Risk of misunderstanding of quwstions in questionnair is more than schedule.
2- Data representation of family expenditure using Pie Chart
3-
X = X1*n1 + X2*n2
n1 +n2
where X = Combined arithmetic mean = 10.9
X1 = arithmetic mean of sample (1) = 10.4 and n1 = No. of sample (1) = 100
X2 = arithmetic mean of sample (1) = ? and n1 = No. of sample (2) = 150
So… 10.9 = 10.4 * 100 + X2 * 150
100 + 150
2725 = 1040 + X2 * 150 1685 = X2 * 150
X2 = 11.23
So the average weight of screws of box B = 11.23
4- (a) As a decision maker in many cases you have to take action about implementing, producing or manufacturing either of one or two or some times more course of actions. With the help of rules of probability you can make...

...Worksheet 1 - Basic Concepts
1. What is Inferential statistics?
Inferential statistics uses observations of past occurrences or available data i.e. descriptive statistics to make decisions about future possibilities and/or the nature of the entire body of data. Inferential statistics draws conclusions or makes interpretations, predictions and inferences about a population based upon an analysis of a sample.
2. Give 2 different techniques which are used in descriptive statistics to represent the data.
Tables or graphs (histograms, boxplots, etc) or numerical summaries
3. Define each of the following terms:
a) Variable
The topics/issues under investigation in statistical analysis. The variable is a characteristic or property of the members of the population which may vary e.g. height, weight, perception etc.
b) Population
The total group about which information is being sought. If information is sought about voting intentions, the population is all those people eligible to vote in an electorate, or a state or the nation.
c) Sample
A sample is a group taken from the population. Most statistical situations do not allow an entire population to be used for analysis (usually because it is too large, the geographical dispersion of subjects, logistical issues, funding, time restraints etc) so a sample must be used. The sample chosen should be representative of and reflect all of the...

...central tendency of the sample.
6. Measures of dispersion: range, the interquartile range, the variance, and the standard deviation. What do these measures tell you about the “spread” of the data? Why is it important to spend time performing basic descriptive statistics prior to conducting inferential statistical tests?
Variance of a sample = S2 = =
Standard Deviation of sample S=
Range is the difference between the highest and the lowest values (250-100) = 150
Interquartile Range takes into consideration the fact that there are data extremes that affect the range. In the case of the data above, most of the values are around the median but two values (250 and 275) are extremes. In this scenario, Interquartile range is a better indication of the dispersion of the distribution
100 100 103 104 105 Q1 107 110 110 114 115 M 115 115 115 115 117 Q2 117 118 120 250 275
• Q1 = (105+107)/2 = 106
• Q2 = (117+117)/2 = 117
• IR = 117-106 =9
It is important to evaluate data and look at the entire picture to determine whether something fits or does not. The fact that we get two measurements that were extreme might be an indication that something may have gone wrong. Descriptive statistics in such a case becomes instrumental in our analysis
Type I and Type II Error: The concept of Type I and Type II Error is critical and will come into play with each statistical test you perform. Discuss the implications of...

...Q-1 STATISTICS PLAYS A VITTAL ROLE IN ALMOST EVERY FACET OF HUMAN LIFE.DECRIBE THE FUNCTIONS OF STATISTIC.EXPLAIN THE APPLICATION OF STATISTICS.
ANS- MEANING OF STATISTICS-
ACCORDING TO SELIGMAN “STATISTIC IS A SCIENCE WHICH DEALS WITH THE METHOD OF COLLECTING, CLASSIFYING, PRESENTING, COMPARING & INTERPRETING THE NUMERICAL DATA TO THROW LIGHT ON ENQUIRY.”
ACCORDING TO CROXTON & COWDEN- “STATISTICS IS THE SCIENCE OF COLLECTION, PRESENTATION, ANALYSIS & INTERPRETATION OF NUMERICAL DATA FROM LOGICAL ANALYSIS.”
FUNCTIONS OF STATISTICS- STATISTICS IS USED FOR VARIOUS PURPOSE, FUNCTIONS ARE-
1- STATISTICS SIMPLIFIES MASS DATA- THE USE OF STSTISTIC CONCEPT HELPS IN SIMPLIFICATION OF COMPLEX DATA.USING STATISTICAL CONCEPT, THE MANAGERS CAN MAKE DECISIONS MORE EASILY. THE STATISTICAL METHODS HELP IN REDUCING THE COMPLEXITY OF THE DATA & IN THE UNDERSTANDING OF ANY HUGE MASS DATA.
2- STATISTICS BRINGS OUT TRENDS & TENDENCIES IN THE DATA- AFTER DATA IS COLLECTED, IT IS EASY TO ANALYSE THE TREND & TENDENCIES IN THE DATA BY USING THE VARIOUS CONCEPT OF STATISTICS.
3- STATISTICS BRING OUT THE HIDDEN RELATIONS BETWEEN VARIABLES- STATISTICAL ANALYSIS HELPS IN DRAWING INFERENCES ON THE DATA.STATISTICAL ANALYSIS BRINGS OUT THE HIDDEN RELATION BETWEEN VARIABLES.
4- DECISION MAKING POWER BECOMES EASIER- WITH THE PROPER APPLICATION OF...