PGDISM-05

Assignment-1
Q1. What is statistics? Discuss the importance and limitation of statistics.
Define sample, parameter and statistics. 


Statistics is concerned with scientific methods for collecting, organizing,

summarizing, presenting and analyzing data as well as deriving valid
conclusions and making reasonable decisions on the basis of this analysis.
Statistics is concerned with the systematic collection of numerical data
and its interpretation. The word ‘statistic’ is used to refer to
1. Numerical facts, such as the number of people living in particular area.
2. The study of ways of collecting, analyzing and interpreting the facts.

IMPORTANCE OF STATISTICS
 Statistics assists in summarizing the larger sets of data in a form
that is easily understandable.
 Statistics assists in sound and effective planning in any field of
inquiry.
 Statistic assists in drawing general conclusions and in making
predictions of hoe much of a thing will happen under given
conditions.
 Statistical techniques being powerful tools for analyzing numerical
data are used in almost every branch of learning.

Limitations of statistics-
1. Statistics is not suitable to the study of qualitative phenomenon
2. Statistics does not study individuals
3. Statistical laws are not exact
4. Statistics table may be misused:
5. Statistics is only, one of the methods of studying a problem
A sample is a smaller group of members of a population selected to
represent the population.
A parameter is a characteristic of a population.
A statistic is a characteristic of a sample.

Q2. Discuss the measures of central tendency and dispersion. 


Various measures of central tendency are:

a. Arithmetic Mean- It is the important, popular and simplest measure

 of central tendency. It is generally known as ‘Mean” alone. It is
obtained by adding the values of all the items of a series and
dividing the total by the number of items.
b. Median- Median of a distribution is that value of the variate which
divides it into two equal parts. Median divides the series in two
equal parts, one half containing values greater than it and other half
containing values less than it. Median is a positional average as its
value depends upon the position of an item and not its magnitude.
c. Mode- It is the value which occurs the greatest number of
frequency in a series. Mode is the most fashionable or typical value
of distribution because it is repeated the highest number of times in
the series. The mode in a distribution is that item around which
there is a maximum concentration.

Various measures of dispersion-

a. Standard Deviation- It is a measure that is used to quantify

the amount of variation or dispersion of a set of data values.
The standard deviation is the square root of its variance. The
standard deviation is commonly used to measure confidence
in statistical conclusions.
b. Range- range of a set of data is the difference between the
largest and smallest values.
c. Mean Deviation- It is a measure of dispersion based on all
observations. It is defined as the arithmetic mean of the
absolute deviations of observations from a central value like
mean, median or mode.

Q3. What is test of significance? Discuss T-test and F-test with suitable
examples.

Once sample data has been gathered through an observational study or

experiment, statistical inference allows analysts to assess evidence in
favor or some claim about the population from which the sample has
been drawn. The methods of inference used to support or reject claims
based on sample data are known as tests of significance.

T-test: A t-test is a form of the statistical hypothesis test, based on

Student’s t-statistic and t-distribution to find out the p-value (probability)
which can be used to accept or reject the null hypothesis.
T-test analyses if the means of two data sets are greatly different from
each other, i.e. whether the population mean is equal to or different from
the standard mean. It can also be used to ascertain whether the regression
line has a slope different from zero.

Mean and standard deviation of the two sample are used to

make comparison between them, such that:

where,
x̄1 = Mean of the first dataset
x̄2 = Mean of the second dataset
S1 = Standard deviation of the first dataset
S2 = Standard deviation of the second dataset
n1 = Size of first dataset
n2 = Size of second dataset

F-Test- F-testis described as a type of hypothesis test, that is

based on Snedecor f-distribution, under the null hypothesis.
The test is performed when it is not known whether the two
populations have the same variance.
F-test can also be used to check if the data conforms to a
regression model, which is acquired through least square
analysis. When there is multiple linear regression analysis, it
examines the overall validity of the model or determines
whether any of the independent variables is having a linear
relationship with the dependent variable. A number of
predictions can be made through, the comparison of the two
datasets. The expression of the f-test value is in the ratio of
variances of the two observations, which is shown as under:
 Assignment-2
Q1. What is a frequency distribution? Explain the diagrammatic and
graphical representation of frequency distribution.

In statistics, a frequency distribution is a list, table or graph that displays

the frequency of various outcomes in a sample. Each entry in the table
contains the frequency or count of the occurrences of values within a
particular group or interval, and in this way, the table summarizes the
distribution of values in the sample. A frequency distribution shows us a
summarized grouping of data divided into mutually exclusive classes and
the number of occurrences in a class. It is a way of showing unorganized
data.

Types of representation of a frequency distribution :

1. Line diagram- We use Multiple line chart for representing two or more
related time series data expressed in the same unit and multiple – axis
chart in somewhat similar situations, if the variables are expressed in
different units.

2. Histogram-A 2-D graphical representation of a continuous frequency

distribution is called a histogram. In histogram, the bars are placed
continuously side by side with no gap between adjacent bars.

3. Bar diagram- There are two types of bar diagrams namely, Horizontal
Bar diagram and Vertical bar diagram.While horizontal bar diagram is
used for qualitative data or data varying over space, the vertical bar
diagram is associated with quantitative data or time series data.Bars i.e.
rectangles of equal width and usually of varying lengths are drawn either
horizontally or vertically.

4. Pie chart- In a pie chart, the various observations or components are

represented by the sectors of a circle and the whole circle represents the
sum of the value of all the components .Clearly, the total angle of 360° at
the center of the circle is divided according to the values of the
components .

5. Frequency polygon- Frequency Polygon is another method of

representing frequency distribution graphically.Obtain the frequency
distribution and compute the mid points of each class interval.Represent
the mid points along the X-axis and the frequencies along the Y-axis.Plot
the points corresponding to the frequency at each mid point.Join these
points, by straight lines in order.To complete the polygon join the point at
each end immediately to the lower or higher class marks (as the case may
be at zero frequency) on the X-axis.

Q2. What is time series? Discuss the components of time series. Discuss
the least square method of finding the trend.

Time series is a sequence of well defined data points measured at

consistent time intervals over a period of time. Values taken by a variable
over time (such as daily sales revenue, weekly orders, monthly
overheads, yearly income) and tabulated or plotted as chronologically
ordered numbers or data points is called time series. To yield valid
statistical inferences, these values must be repeatedly measured.

Time series consist of four components:

(1) Seasonal variations that repeat over a specific period such as a day,
week, month, season, etc.,

(2) Trend variations that move up or down in a reasonably predictable

pattern,

(3) Cyclical variations that correspond with business or economic 'boom-

bust' cycles or follow their own peculiar cycles, and

(4) Random variations that do not fall under any of the above three
classifications.

Least Square Method-

The least squares method is a form of analysis that finds the line of best
fit for a dataset, providing a visual demonstration of the relationship
between the data points. Each point of data is representative of the
relationship between a known independent variable and an unknown
dependent variable.

The least squares method provides the overall rationale for the placement
of the line of best fit among the data points being studied. The most
common application of the least squares method, referred to as linear or
ordinary, aims to create a straight line that minimizes the sum of the
squares of the errors generated by the results of the associated equations,
such as the squared residuals resulting from differences in the observed
value and the value anticipated based on the model.

Q3. Define random variable. Explain the types of probability

distributions.

A random variable is a variable whose value is unknown, or a function

that assigns values to each of an experiment's outcomes. A random
variable's possible values might represent the possible outcomes of a yet-
to-be-performed experiment, or the possible outcomes of a past
experiment whose already-existing value is uncertain.

Types of Probability distribution-

1. Binomial Distribution- A Binomial distribution is a probability

distribution expressing the probability of one set of dichotomous
alternatives, e.g. success of failure. The essential features of
binomial distribution can be stated in a general manner which
enables the distribution to be used in a wide variety of
circumstances. It is appropriate in any situation which involves n
independent trials of random experiment, with two possible
outcomes of each trial.
2. Poisson Distribution- The poisson distribution is based on same
assumptions as the binomial distribution. This means that in a
Poisson experiment we deal with either the success or failure, that
the successes are independent of each other, and thus the
probability of success throughout the entire process remains
constant. It is applicable where there are number of random
situations where probability of a success on a single trial and the
number of trials is large.
3. Normal Distribution- It is most useful probability distribution for
continuous variables. The probability distributions of most sample
statistics are derived and closely connected with normal
distribution. It has convenient mathematical properties and it also
serves as an approximation to other discrete probability
distributions.
 PGDISM-06

Assignment-1

Q1. Discuss in short the safety provisions of Boiler Act, 1923 


The regulation would cover not only inspection but also the material
procurement.

A typical safety provisions includes the following stages:

(1)Design Review-The manufacturer contacts the inspection authority for

approval of boiler or boiler component design. Inspecting authority
provides feedback on the design to ensure they meet IBR. After both the
manufacturer and Inspecting authority are satisfied the design is sent to
the Central Boilers Board and the Chief Inspector of Boilers of the Indian
state in which the boiler or components is to be installed.

(2)Material Inspection-Inspecting authority inspects the pressure part

materials (plates, pipes, tubes, castings, forgings fittings, standard parts,
etc.) and signs the relevant certificate forms.

(3)Pressure part inspection-The inspecting authority carries out stage

inspections during the manufacture of a boiler or boiler components.

(4)Qualification test for welders-Welders engaged in the manufacture and

site welding connected with erection and fabrication and repair of boilers
shall be qualified by a Competent

Q2- Explain the role of Director General in administration for Factories

Act, 1923.

Rendering advice and carrying out support research activities for the
administration of the Factories Act, 1948 and the Workers (Safety, Health
and Welfare) Act, 1986.

Co-ordinating technical and legal activities to facilitate uniform

standards of enforcement of safety and health in manufacturing and port
sectors.

Administration of the Workers (Safety, Health & Welfare) Act, 1986

and Regulations framed there under and enforcing these in the major
ports of the country.

Educating and training employers and employees on matters relating to

safety and health.

Conducting promotional activities by operating schemes for (i)

recognition of good suggestions under Vishwakarma Rashtriya Puraskar
and good (ii) worker’s outstanding contribution in organizations, under
Prime Minister’s Shram Awards; and (iii) safety performance under
National Safety Awards (on behalf of the Ministry).

Co-operating with International agencies like ILO, WHO, UNDP and

advising Central Government in the adoption of international standards
concerning safety and health.

Training of foreign nationals and rendering expert advice to

developing countries.

Building Competence of enforcement agencies.

Issuing approval to flameproof electrical enclosures.

Collecting and disseminating information and material relating to

safety and health.

Q3- Discuss the role ILO in promoting the uniform safety standards.

The ILO has prepared and published a series of codes of practice relating
to various sectors of economic activity and various types of dangerous
equipment or agents. Presented in the form of detailed technical
specifications, these publications are intended to assist governments,
employers' and workers' organizations in drawing up national regulations
and guidelines, work regulations and collective agreements. They also
suggest practical solutions for the application of ILO international
standards. The recommendations they contain are usually finalized and
approved by tripartite panels of experts.

More than 35 codes of practice have been drawn up so far, covering

either different sectors of activity (such as mines, agriculture, forestry,
construction, iron and steel, etc.) or particular risks (ionizing radiations,
noise and vibration, exposure to airborne substances, use of synthetic
vitreous fibre insulation wools), as well as transfer of technology.
Codes of practice indicate "what should be done". They are prepared by
tripartite meetings of experts and their publications are approved by the
ILO Governing Body.

Assignment-2

Q1- “Safety and health standards are complimentary”. Justify the

statement in the light of OSHA.

Employers have the responsibility to provide a safe workplace.

By law, employers must provide their workers with a workplace that does
not have serious hazards and must follow all safety and health standards.
Employers must find and correct safety and health problems. OSHA
requires that employers must first try to eliminate or reduce hazards by
making feasible changes in working conditions rather than relying on
personal protective equipment such as masks, gloves, or earplugs.
Switching to safer chemicals, enclosing processes to trap harmful fumes,
or using ventilation systems to clean the air are examples of effective
ways to eliminate or reduce risks.

Employers must:

 Inform workers about chemical hazards through training, labels,

alarms, color-coded systems, chemical information sheets and
other methods.
 Provide safety training to workers in a language and vocabulary
they can understand
 Keep accurate records of work-related injuries and illnesses.
 Perform tests in the workplace, such as air sampling, required by
some OSHA standards.
 Provide required personal protective equipment at no cost to
workers.

Q2- Discuss pertinent provisions of the Workmen’s Compensation Act,

1923.

The Workmen’s Compensation Act provides provisions for compensation for:

1) Death
 2) Permanent total disablement;

3) Permanent partial disablement; and

4) Temporary disablement – total or partial.

1) Compensation for Death: Where death results from an injury, the amount
of compensation shall be equal to 50 percent of the monthly wages of the
deceased workman multiplied by the relevant factor, or Rs. 85,000 whichever
is more.

2) Compensation for Permanent Total Disablement: Where permanent total

disablement results from an injury, the amount of compensation payable shall
be equal to 60 percent of the monthly wages of the injured workman
multiplied by the relevant factor, or Rs. 90,000, whichever is more.

3) Compensation for Permanent Partial Disablement: i) In the case of an

injury specified in Part II of Schedule I, the percentage of compensation
payable is proportionate to the loss of earning capacity permanently caused by
the Scheduled injury. Thus, if the loss of earning capacity caused by an injury
specified in Part II of Schedule I is 30 percent, the amount of compensation
shall be 30 percent of compensation payable in case of permanent total
disablement.

ii) In the case of an injury not specified in Schedule I such percentage of the
compensation payable in the case of permanent total disablement as is
proportionate to the loss of earning capacity permanently caused by the injury.

4) Compensation for Temporary Disablement: A half monthly payment of the

sum whether total or partial results equivalent to 25% of monthly wages of the
from the injury workman to be paid in the manner prescribed.

Q3- Critically appraise the rules and regulations related to safety in

chemical industry.

Rules and regulations in chemical industry are taken in consideration as

under:

1. Plant Layout- Plant layout has some specific safety aspects.

Examples include:

Separation and isolation-Chemicals which may react with one another are
to be physically separated, oxidizers are to be stored in areas remote from
fuel storage. Areas of potential explosions storage of explosives, reaction
vessels are to be isolated so if there is an explosion, the damage and risk
to employees is minimized.

Drainage-Where hazardous liquids may leak or spill from piping or

vessels, what provisions are made to prevent their spread to areas where
employees may be exposed to the hazard? Examples of possible methods
include diking and grading.

Housekeeping- Are work areas well maintained?

Enclosed spaces- Some processes which are safe in open air may become
hazardous if enclosed. If areas of potential or frequent leaks or spills are
enclosed to prevent environmental contamination or the spread of the
chemicalk, are there adequate precautions to protect employees?

2. Materials Compatibility- At least two factors should be considered in

materials selection: First, will the contaminate or cause a reaction in the
chemicals to be handled or processed? Second, will the chemicals to be
processed attach or destroy the equipment? For all chemical processes:
there are preferred materials; preferences sometimes are economic, and
sometimes they arc based on chemical reactivity or compatibility. The
intent here is to identify readily available materials that might be used but
that are incompatible with the chemicals involved.

3. Contamination Control- Potentially reactive chemicals may have their

reactions catalyzed by common materials which easily enter systems
whenever seals are opened.

4. Physical Facilities- Much plant equipment could be considered

ancillary to the production processes. Examples of systems that may need
to be present, properly inspected, and functional are:

Emergency eye wash or shower.

Fixed fire suppression equipment.

Portable firefighting equipment, if employees or a fire brigade are to use

portable firefighting equipment.

5. Inspection and Maintenance- All equipment must be shut down

sometime, no matter how infrequently. Pressure vessels also need
periodic inspection and testing because of normal wear and potential
corrosion either at welds or in the base material. The combination of
pressure and volume determine the hazard: high volume, low pressure
systems can have the same potential energy for release as low volume,
high pressure systems.