Statics for management

Que:1

Define “Statistics”. What are the functions of Statistics? Distinguish between
Primary data and Secondary data.

Ans:
 Statistics
Statistics is a mathematical science pertaining to the collection, analysis, interpretation
or explanation, and presentation of data. It also provides tools for prediction and
forecasting based on data. It is applicable to a wide variety of academic disciplines, from
the natural and social sciences to the humanities, government and business.

Statistical methods can be used to summarize or describe a collection of data; this is
called descriptive statistics. In addition, patterns in the data may be modeled in a way
that accounts for randomness and uncertainty in the observations, and are then used to
draw inferences about the process or population being studied; this is called inferential
statistics. Descriptive, predictive, and inferential statistics comprise applied statistics.

There is also a discipline called mathematical statistics, which is concerned with the
theoretical basis of the subject. Moreover, there is a branch of statistics called exact
statistics that is based on exact probability statements.

The word statistics can either be singular or plural. In its singular form, statistics refers
to the mathematical science discussed in this article. In its plural form, statistics is the
plural of the word statistic, which refers to a quantity (such as a mean) calculated from a
set of data.

 Management

In all business and organizational activities is the act of getting people together to
accomplish desired goals and objectives using available resources efficiently and
effectively.

Management comprises planning,organizing,staffing,leading or directing, and controlling
an organization(a group of one or more people or entities) or effort for the purpose of

accomplishing a goal. Resourcing encompasses the deployment and manipulation of
human resources,financial resources,technological resources, and natural resources.

Since organizations can be viewed as systems,management can also be defined as
human action, including design, to facilitate the production of useful outcomes from a
system. This view opens the opportunity to 'manage' oneself, a per-requisite to
attempting to manage others. Management operates through various functions, often
classified as planning, organizing, staffing, leading/directing, controlling/monitoring and
motivation.

 Planning:
It Deciding what needs to happen in the future (today, next week, next month, next
year, over the next five years, etc.) and generating plans for action.

 Organizing :
(Implementation) making optimum use of the resources required to enable the
successful carrying out of plans.

 Staffing:
Job analysis, recruitment, and hiring for appropriate jobs.

 Leading/directing :
Determining what needs to be done in a situation and getting people to dot.

 Controlling/monitoring:
Checking progress against plans.

 Motivation:
Motivation is also a kind of basic function of management, because without motivation,
employees cannot work effectively. If motivation does not take place in an organization,
then employees may not contribute to the other functions (which are usually set by top-
level management).
Basic roles

 Interpersonal:
Roles that involve coordination and interaction with employees.

Difference between primary and secondary data :

Primary Data

1. Primary data are always original as it is collected by the investigator.

2. Suitability of the primary data will be positive because it has been systematically
collected.

3. Primary data are expensive and time consuming.

4. Extra precautions are not required.

5. Primary data are in the shape of raw material.

6. Possibility of personal prejudice.

Secondary Data

1. Secondary data lacks originality. The investigator makes use of the data collected by
other agencies.

2. Secondary data may or may not suit the objects of inquiry.

3. Secondary data are relatively cheaper.

4. It is used with great care and caution.

5. Secondary data are usually in the shape of ready made products.

6. Possibility of lesser degree of personal prejudice.

Que:2

Draw a histogram for the following distribution:

Age
Age 0-10 10-20 20-30 30-40 40-50

No. Of 2 5 10 8 4
People

Age No of People
0-10 2
10-20 5
20-30 10
30-40 8
40-50 4

histogram diagram
12

10

8

6
o
p
e
l

4

2

0
10 20 30 40 50

Age

Que:3

Find the (i) arithmetic mean and (ii) the median value of the following set of
values: 40, 32, 24, 36, 42, 18, 10.

(i)The arithmetic mean
̅x=Σ fixi/ Σfi

(40+32+24+36+42+18+10)/7
=28.85

(ii)Median value

10,18,24,32,36,40,42
N=7
Median =(N+1)/2 th
=(7+1)/2
=4
M=32

Que:4

Calculate the standard deviation of the following data:

Marks 78-80 80-82 82-84 84-86 86-88 88-90

No. Of 3 15 26 23 9 4
Students

Class Mead valueX Frequency ‘f’ d=X-83/2 fd fd²
interval
78-80 79 3 -2 -6 12

80-82 81 15 -1 -15 15

82-84 83 26 0 0 0

84-86 85 23 1 23 23

86-88 87 9 2 18 36

88-90 89 4 3 12 36

80 32 122

σ²=[Σfd²/n-[Σfd/Σf]²]x(C.I)²
σ²=[122/80-[32/80]²]x4=5.46
standard deviation=σ=2.336

Que:5

Explain the following terms with respect to Statistics: (i) Sample, (ii) Variable,
(iii) Population.

(i)Sample

 In statistics,a sample is a subset of a population .Typically, the population is very large,
making a census or a complete enumeration of all the values in the population impractical or
impossible.

 The sample represents a subset of manageable size. Samples are collected and statistics are
calculated from the samples so that one can extrapolation sample to the population. This
process of collecting information from a sample is referred to as sampling.

 A complete sample is a set of objects from a parent population that includes ALL such
objects that satisfy a set of well-defined selection criteria.

 For example, a complete sample of Australian men taller than 2m would consist of a list of
every Australian male taller than 2m. But it wouldn’t include German males, or tall Australian
females, or people shorter than 2m. So to compile such a complete sample requires a
complete list of the parent population, including data on height,gender and nationality for
,
each member of that parent population.

 In the case of human populations, such a complete list is unlikely to exist, but such complete
samples are often available in other disciplines, such as complete magnitude-limited samples
of astronomical objects.

 An unbiased sample is a set of objects chosen from a complete sample using a selection
process that does not depend on the properties of the objects. For example, an unbiased
sample of Australian men taller than 2m might consist of a randomly sampled subset of 1%
of Australian males taller than 2m. But one chosen from the electoral register might not be
unbiased since,

 For example, males aged under 18 will not be on the electoral register. In an astronomical
context, an unbiased sample might consist of that fraction of a complete sample for which
data are available,provided the data availability is not biased by individual source properties.
The best way to avoid a biased or unrepresentative sample is to select a random sample also
known as a probability sample

 A random sample is defined as a sample where each individual member of the population
has a known, non-zero chance of being selected as part of the sample. Several types of
random samples are simple random samples, systematic samples, stratified random
samples,and cluster random samples

(ii)Variable

 A variable is a characteristic that may assume more than one set of values to which a
numerical measure can be assigned. Height, age, amount of income, province or country of
birth, grades obtained at school and type of housing are all examples of variables. Variables
may be classified into various categories,some of which are outlined in this section.

Categorical variables:

 A categorical variable (also called qualitative variable) is one for which each response can be
put into a specific category. These categories must be mutually exclusive and exhaustive.
Mutually exclusive means that each possible survey response should belong to only one
category, whereas, exhaustive requires that the categories should cover the entire set
of possibilities. Categorical variables can be either nominal or ordinal.

Nominal variables:

 A nominal variable is one that describes a name or category. Contrary to ordinal variables,
there is no 'natural ordering' of the set of possible names or categories.

Ordinal variables:

 An ordinal variable is a categorical variable for which the possible categories can be placed in
a specific order or in some 'natural' way.

Numeric variables:

 A numeric variable,also known as a quantitative variable, is one that can assume a
number of real values such as age or number of people in a household. However, not all
variables described by numbers are considered numeric. For example, when you are asked
to assign a value from 1 to 5 to express your level of satisfaction, you use numbers, but the
variable(satisfaction) is really an ordinal variable. Numeric variables may be either continuous
or discrete.

Continuous variables:

 A variable is said to be continuous if it can assume an infinite number of real values.
Examples of a continuous variable are distance, age and temperature. The measurement
of a continuous variable is restricted by the methods used, or by the accuracy of the
measuring instruments. For example, the height of a student is a continuous variable
because a student may be 1.6321748755... meters tall.

Discrete variables:

 As opposed to a continuous variable, a discrete variable can only take a finite number of
real values. An example of a discrete variable would be the score given by a judge to a
gymnast in competition: the range is 0 to 10 and the score is always given to one decimal

(iii)Population

 A statistical population is a set of entities concerning which statistical inferences are to be
drawn, often based on a random sample taken from the population.

 For example, if we were interested in generalizations about crows,then we would describe
the set of crows that is of interest. Notice that if we choose a population like all crows, we will
be limited to observing crows that ulatixist now or will exist in the future.

 Probably,geography will also constitute a limitation in that our resources for studying crows
are also limited. Population is also used to refer to a set of potential measurements or
values, including not only cases actually observed but those that are potentially observable.

 Suppose, for example, we are interested in the set of all adult crows now alive in the county
of Cambridge shire,and we want to know the mean weight of these birds. For each bird in
the population of crows there is a weight, and the set of these weights is called the population
of weights.

 A subset of a population is called a sub population. If different sub populations have different
properties, the properties and response of the overall population can often be better
understood if it is first separated into distinct sub populations.

 For instance, a particular medicine may have different effects on different sub populations,
and these effects may be obscured or dismissed if such special sub populations are not
identified and examined in isolation.

 Similarly, one can often estimate parameters more accurately if one separates out sub
populations: distribution of heights among people is better modeled by considering men and
women as separate sub populations, for instance.

 Populations consisting of sub populations can be modeled by mixture models,which
combine the distributions within sub populations into an overall population distribution.

Que:6

An unbiased coin is tossed six times. What is the probability that the tosses will
result in: (i) at least four heads, and (ii) exactly two heads

Let ‘A’ be the event of getting head. Given that:

(iI) The probability that the tosses will result in exactly two heads is given by:

herefore, the probability that the tosses will result in exactly two heads is 15/64.

(I)probability of at least four heads

P(X>=4) =P(X=4)+P(X=5)+P(X=6)
= 22/64=11/32

Master of Business Administration- MBA
Semester 1

MB0038 –Statics For Management–
4 Credits

(Book ID:B1127)

Assignment Set- 1 (60 Marks)

Statics for management

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Statics for management