Here is Statistics REDUCED SYLLABUS for HSSC II, class 12
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STATISTICS-XII Reduced syllabus 2020-21
1. Probability (1/8)
Content Scope
Brief revision of set theory, random
experiment, sample space, events. Axiomatic
and relative definition of probability.
Conditional probability, multiplication
theorem, (without proof) independence,
application of addition theorem, counting rules,
permutations and combinations and their real world
problems involving the computation of
probabilities.
In explaining ‘basic concepts’, givehe
difference between certainty and uncertainty
by examples. Examples shall be selected from
areas such as, business. Medicine, Agriculture,
Astronomy, Psychology, etc. Also the
applications of probability for prediction and
forecasting be highlighted.
Addition theorem of two events conditional
probability, multiplication theorem be
explained with the help of bivariate tables.
Concept of independence be explained using
classical logic through coins and dice as well
as real events.
In counting problems many examples be given
for the calculation of number of combinations
and permutations. The multiplication method
of counting be explained through examples.
While explaining applications of probability
from real world problems, exercise be selected
from different scientific fields such as
Medicine, Meteorology, Engineering
Agriculture, Space Sciences etc.
2. Discrete and continuous probability distribution
(2/8)
Content Scope
Concept of random variable, discrete univariate
probability distributions, joint and marginal
probability, expectation and variance of
discrete random variables, discrete uniform
distributions generation and application of
random numbers, continuous univariate
probability distributions through geometrical
concepts.
Explain random variable by sample space,
variable and probability. Explain the difference
between mathematical variable and random
variable: random variables can be discrete or
continuous. Examples of random variables like
number of patients in a clinic per day, number
of accidents on a given road per weak, number
of plants without followers per square yard in a
given fields etc, be explained as real world
examples of random variable.
In discussing discrete variate: “Probability
distribution expectation and variance”, use
frequency tables for head and tails in coins,
number of defective items in lots of five items
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etc, number of accidents per week on a certain
road. Discrete uniform distribution to be
discussed through random numbers which
should be generated or obtained from random
number tables. Discrete uniform distribution
would thus be obtained and mean variance
would be obtained from there. While doing this
random number table on one page or more than
one pages may be used. “Continuous univariate
probability distributions”, would be those
which can be sketched through linear functions
such as F(x) = x + a from the lower limit
would be shown equating to one, and areas on
smaller intervals would be shown as values of
probability
3. Hypergeometric and Binominal Probability,
Distributions (1/8)
Contents Scope
Bernoulli trails, Binominal distribution, its
mean, variance, skewness and applications.
Hypergeometric experiments to be explained
through examples such as selecting a number
of fish of particular type from a large pond,
selecting a set of defective items from a
production belt in a factory etc.
Hypergeometric distribution to be explained
using “M” balls in a box out of which “k” balls
are white and (M-k) balls are black and “n”
balls are drawn from the box, the probability
expression would be explained. Special cases
for specific values of “N”, “k” and “n” to be
obtained. The expression for the mean and the
variance of hyper geometric distribution to be
given without derivation but to be explained
thoroughly, “Bernoulli trails to be explained
using black and white balls in a box, head and
tail in case of a coin, boy and girl in a family,
defective and nondefective items in a given
large lot, sick and healthy people in a town etc.
The evens would be defined in terms of the
result of a given number of trails such as
(HTTHH) occurring in a five trails from five
losses of coin. The number of heads, the
number of balls of a particular colour in a
selection of (say ) 10 balls, etc be defined as
the Binominal variable. The Binominal
probability distribution to be explained by first
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explaining Bernoulli trails, the mean and
variance be derived. In the exercises, problems
must be selected from fields such as Medicine,
Agriculture, Engineering, Geology, Pharmacy
and Psychology etc.
4. Normal Distribution (1/8)
Content Scope
Normal probability distribution and its
properties, computation of probabilities (areas
under the National Curve), applications in real
life, kurtosis.
Normal Probability distribution to be explained
by writing the mathematical function with its
parameters. The sketches of the normal
distribution to be explained by :
i. Keeping parameter of mean as fixed and
changing the standard deviation.
ii. Keeping the parameter of standard
deviation as fixed and changing the
parameter of mean. The standard normal
distribution be explained and the tables of
areas under the standard normal
distribution be explained. Exercise be
given so that for given intervals areas are
obtained with the use of normal tables and
also intervals are obtained when
probabilities are given. Exercise based on
fields such as, Medicine, business,
agriculture, Psychology, Economics etc.,
be solved in sufficient number.
5. Sampling and sampling distribution (1/8)
Content Scope
Population and sample: advantages of
sampling; sampling error and non-sampling
error; probability and non-probability sampling
sample random and stratified random
sampling.
Population and sample, advantages of
sampling” be explained by stating that
populations are usually large and not generally
possible to observe each and every member of
it. This problem be explained as kind of
difficult situation to be solved. The importance
of random sample be explained, which gives
accurate results for the parameters of the
population and is a useful statistical procedure
to arrive at almost accurate results sampling be
also explained as a useful technique for
prediction.
“Sampling error”, be explained as the amount
of error that would occur while drawing the
sample,. The measurement of sampling error
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be explained as a useful way of knowing the
precision of the index, which is derived from
the sample.
“Non sampling error” be explained as those
errors which cannot be eliminated. These occur
in cases when there is a fault in the measuring
scale or the observation kit. Examples of
sampling be given from fields such as
Agriculture, Medicine, Psychology, Economics
etc.
Selection of all possible samples from finite
population with and without re-placement,
parameter and statistic, sampling distributions
of mean and proportion, concept of Central
Limit Theorem.
Explain the sampling distribution of the mean
by first showing that sample mean is a random
variable. In order to do this, selection of all
possible samples from finite populations with
and without replacement be explained. Explain
the terms parameter and statistic as quantities
related with the population and sample
respectively. The sampling distribution of the
variance be explained through examples based
on a small set of observations. In the same
way, the sampling distribution of proportion be
explained also.
Central limit theorem be explained to show the
shape location and dispersion of the
distribution of the sample mean when samples
are large and when the distribution of the
population is unknown or known to be nonnormal.
6. Statistical inference (1/8)
Content Scope
Concept of statistical Inference: Point
estimation of the population mean, variance
and proportion: unbasedness of mean and
proportion intervals for the mean of a normal
population (known and unknown standard
deviation), confidence interval of proportion
(large samples).
Formulation of Alull and alternative
hypotheses: type-I and type-II error, test of
hypotheses for the mean of a normal
population (known and unknown standard
deviation).
Explained standard inference by showing that
the mean and variance parameters in a
population are mostly unknown. Explain that
mostly, samples are only available. Discuss the
techniques of inference as a set of statistical
procedures by which unknown parameters of
the given population are estimated. Parameters
be explained as point estimators, confidence
interval, hypothesis to be tested. Explain point
estimation of the population mean, variance
and proportion by considering a finite
population of four of five observations and by
writing all the samples of two or three or four
observations. Mean and variance be explained
85
For population mean and proportion (large
samples)
with reference to such finite of mean and
proportion explained with such finite
populations as well.
Explain the confidence Interval for the mean of
a normal distribution when standard deviation
is known by writing the probability express for
standard normal variable on an interval and
then converting it into a confidence interval
and of “Mean”, When standard deviation is
unknown, use of distribution and variable be
explained.
For population mean and proportion when the
distribution is not given, large samples be
considered so that central limit theorem could
be applied. Explain the confidence Interval for
the difference between means and proportions
by considering large independent samples, s
that central limit theorem is applicable.
Explain Null hypothesis in its different forms
i.e., simple and composite one sided and two
sided. Explain the Test by considering sample
mean and sample proportion. Type-I error and
its probability X and Type-II error with its
probability B be explained by using sketches of
Normal Probability Curve. Calculation of X
and B is not required. Test of hypothesis for
the mean of the Normal Population be
discussed by writing the steps (usually 8 or 9).
Use of sketches be encouraged.
7. Association (1/8)
Contents Scope
Concept of categorical or qualitative data
Bivariate categorical (qualitative) data;
association versus independence of two
qualitative variables; (Nominal and ordinals
scales), contingency table; chi-square test of
independence. Measurement of association
between two qualitative variables through the
method of rank correlation co-efficient.
Explain the categorical data by considering
categories in a unvariate case and in a bivariate
case. It may further be explained using nominal
and ordinal scales. It be explained that the most
important statistical analysis in this type of
data is known as association or independence.
Real life examples be considered to explain
various types of data. Explain the calculation
of expected frequencies in a univariate and
bivariate contingency table. Calculation of chi
square to be explained by considering
examples of un-variate and bivariate tables.
Explain with examples the situation, where
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observations are ranked or ordered. Examples
where two judges rank a group of competitors
in a flower arrangement competition, the
ranking of competitors in a fashion show or
dish competition of food dishes or in
competitions of paintings etc. The formula of
rank correlation be given and applied in severa REDUCED
LIST OF PRACTICAL
STATISTICS
The following topics will be included in the syllabus
of practicals:
1. Probability, discrete and continuous probability
distribution.
2. Binomial and normal distribution.
3. Statistical inference, association.
Note:
Two marks will
be reserved for the Practical Note Book. The Note Book must contain a
minimum of Nine practical according to the pattern and
guidelines given below:
Three marks will be reserved for Viva voce. Viva will
be conducted in the Examination
hall with reference to the practical contained in the
Note Book and /or the practicals contained in examination hall.
THE END
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