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Saturday 17 October 2020

STATISTICS REDUCED SYLLABUS, CLASS 12, ONLINE| fbise year 2021-fusion stories

 

Here is Statistics REDUCED SYLLABUS for HSSC II,  class 12

A reduced syllabus of Statistics HSSC has been uploaded on fbise website.


You can check online fbise Statistics reduced syllabus class 12 from here:

STATISTICS-XII Reduced syllabus 2020-21

1. Probability (1/8)

Content Scope

Brief revision of set theory, random

experiment, sample space, events. Axiomatic

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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

83

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

84

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

86

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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