TBSE Class 12 Syllabus 2024 Statistics

Syllabus
Class XII
Sub : Statistics (Theory & Practical)
Half Yearly Exam : 2023-24
Theory Exam : Full Marks : 70, Time : 3 Hours

Mathematics : Limit, Continuity, Differentiation, Integration (only Numerical), Standard
definition of Gamma integral 4 results involving it (without derivation).

Correlation & Regression : Bivariate Data, Scatter diagram, Correlation & Correlation
coefficient, Properties of correlation coefficient, Rank correlation, spearmani & Rank
Correlation coefficient (without tie) .

Concept of Regression, Principle of least & squares, Fitting of Regression lines, Important
results relating to regression lines.

Probability & Probability Distribution –I

Random experiment, Trial, Sample space, Sample point and different types of events,
Definition of Probability : Classical, Statistical, and Axiomatic, Theorem on the probability of
union of time or three events. Conditional Probability, Theorem on Conditional Probability
for two or three events, Independent events, Bayes’ theorem and its application. Random
variable (diserate & continuous) and its probability distribution, cumulative distribution
function. Probability mass function & Probability density function, Mathematical expectation.
Addition and Multiplication rule of mathematical expectation. Problems related to probability
distribution and Mathematical expectation.

Marks distribution for Half Yearly Exam :
Topic 1 Mark 2 Marks 3 Marks 5 Marks

Mathematics 2 1 1 1

Correlation & Regression 5 1 4 3

Probability & Probability Distribution 3 4 1 2

10 12 18 30

Total marks 70

Practical Exam Syllabus for Half -Yearly Exam :

1. Correlation coefficient & linear regression
2. Spearman & Rank correlation coefficient (without tie)
3. Application & Fitting of Binomial distribution
4. Application & fitting of poisson distribution
5. Scatter diagram

Class -XII
Sub: STATISTICS (Theory & Practical)

Pre-Board / Board Final Examination, 2023-24
Theory Examination, Full Marks: 70, Time: 3 Hours

Mathematics: Limit, Continuity, Differentiation, Integration (Only Numerical), Standard
definition of Gamma integral and results involving it (without derivations).

Correlation & Regression

Bivariate data. Scatter diagram. Correlation & Correlation coefficient. Properties of
Correlation coefficient. Rank Correlation, Spearman’s Rank Correlation coefficient (without
tie).

Concept of Regression. Principle of Least squares. Fitting of Regression lines. Important
results relating to regression lines.

Probability & Probability Distributions-I

Random experiment, Trial, Sample space, Sample point and different types of events.
Definition of Probability: Classical, Statistical and Axiomatic. Theorem on the probability of
union of (two & three) events. Conditional probability. Theorem on conditional probability
for two & three events. Independence of events. Bayes’ theorem and its application.

Random variable (discrete and continuous) and its probability distribution. Cumulative
distribution function. Probability mass function and Probability density function.
Mathematical expectation. Addition and Multiplication rule of mathematical expectation.
Problems related to probability distribution and mathematical expectation

Probability Distribution-II

Uniform (Discrete and Continuous), Bernoulli, Binomial, Poisson, Geometric, Normal
distribution and Exponential Distribution.

Sampling, Estimation & Testing of Hypotheses

Population & sample. Parameter & statistic. Census & Sample survey. Concepts of
probability sampling and random number tables. Concepts of sampling distribution of
statistic and its standard error. Chi-square distribution, t-distribution, F-distribution
(Definition and properties only). Simple random sampling with replacement (SRSWR) and
Simple random sampling without replacement (SRSWOR): Estimation of population mean
and standard error of the estimates.

Concept of Point estimation. Requirement of good estimator: Unbiasedness, Consistency,
Efficiency. Elementary concept of MVUE & BLUE.

Statistical tests of Hypothesis- Null & alternative hypothesis. Simple & composite
hypothesis, Critical region, Type-I and Type-II errors, Level of Significance and size of
critical region, Power of a test. Tests of significance related to a single Binomial proportion,
two binomial proportions using large sample approximations. Exact tests of hypothesis under
normal set-up for a single mean and equality of two means. Frequency Chi-square test &
Goodness of fit.

Marks Distribution for Pre-Board/Board Final Examination
Topic 1 Mark 2 Marks 3 Marks 5 Marks
Mathematics NIL NIL NIL 1
Correlation & Regression 2 NIL 1 1
Probability & Probability
Distributions-I 5 2 2 1
Probability Distributions-II NIL 2 2 1
Sampling, Estimation ,
Testing of Hypothesis 3 2 1 2
10 12 18 30
Total marks 70

Practical Examination syllabus of Pre-Board/Board Final Examination
1. Scatter diagram.

2. Correlation coefficient and Linear Regression.

3. Spearman’s Rank Correlation coefficient (without tie).

4. Applications and Fitting of Binomial Distributions.

5. Applications and Fitting of Poisson Distributions.

6. Applications and Fitting of Normal Distributions.

7. Drawing of random samples by using random number tables.

8. Calculation of sample mean and standard error of sample mean in case of SRSWR
and SRSWOR

9. Large sample tests of a single mean, single proportion and difference of two
proportions.

10. Pearson’s Chi-square tests.

11. Exact tests of hypotheses under normal set-up for a single mean, difference of two
means and single variance.

Sub: Statistics
Marks Distribution of Practical Examination
(Half Yearly/Pre-board/Board Final Exam,2023-24)

Full Marks: 30, Time: 3 Hours
1. Experiments (5 + 5 + 5+5) 20 Marks

2. Practical Note Book (PNB) 3 Marks

3. Viva-Voce 2 Marks

4. Attendance 5 Marks

Total Marks :- 30 Marks

U<MA ~:Syllabus fo r Pre-test Examination
Theory Examination, Full Marks: 70, Time: 3 Hours

Unit I: Mathematics

Basic concept of Limit, Continuity, and Differentiability. First and second order derivatives
of a variety of non-trigonometric univariate functions. Maximum and minimum of a variety
of non-trigonometric univariate functions.

Integration of a variety of non-trigonometric univariate functions by substitutions, by partial
fractions and by parts. Standard definition of gamma integral and results involving it (without
derivatives).

Unit II: Correlation & Reg ression

Bivariate data. Scatter diagram. Correlation & Correlation coefficient. Properties of
Correlation coefficient. Rank Correlation, Spearman's Rank Correlation coefficient (without
tie).

Concept of Regression. Principle of Least squares. Fitting of Regression lines. Important
results relating to regression lines.

Unit lll: Probability & Probability Distributions

Random experiment, Trial, Sample space, Sample point and different types of events.
Definition of Probability: Classical, Statistical and Axiomatic. Theorem on the probability of
union of (two & three) events. Conditional probability. Theorem on conditional probability
for two & three events. Independence of events. Bayes' theorem and its application.

Random variable (discrete and continuous) and its probability distribution. Cumulative
distribution function. Probability mass function and Probability density function.
Mathematical expectation.

Uniform (Discrete and Continuous), Bernoulli, Binomial, Poisson, Geometric, Exponential
and Normal distributions.

Unit V: Population Studies

Vital events, rates and ratios. Measurement of Mortality: Crude, Specific and Standardised
death rates, Infant mortality rate. Measurement of Fertility and reproduction: Crude birth rate,
General, Specific and Total fertility rates. Gross and Net reproduction rates.

Unit wise Question Types with Marks Distribution of Pre-test Theory Examination

Unit Title MCQ/Objective SA-I SA-II LA Total
I Mark 2 Mark 3Mark SMark Marks
I Mathematics 4 2 I 2 21
II Correlation & I 2 2 I 16
Regression
llI Probability & 2 1 3 3 28
Probability
Distributions
v Population Studjes 3 I - - 05
Question wise Marks 10 12 18 30 70
distribution

Practical syllabus for Pre-test Examination

Three experiments to be given in the examination as follows:

I. Scatter diagram. Correlation coefficient and Linear Regression.

2. Speannan' s Rank Correlation coefficient (without tie).

3. Applications and Fitting of Binomial Distributions.

4. Applications and Fitting of Poisson Distributions.

5. Applications and Fitting ofNormal Distributions.

6. Calculation of different rates and ratios of fertility, mortality and measures of
reproduction.

Marks Distribution of Pre-test Practical Examination

Full Marks: 30, Time: 3 Hours

I. Experiments (5 + 5 + l 0) 20 Marks

2. Practical Note Book (PNB) 5 Marks

3. Viva-Voce 5 Marks

Syllabus for Test Examination

Theory Examination, Full Marks: 70, Time: 3 Hours

Unit IV: Sampling, Estimation & Testing of Hypotheses

Population & sample. Parameter & statistic. Census & Sample survey. Concepts of
probability sampling and random number tables. Concepts of sampling distribution of
statistic and its standard error. Simple random sampling with replacement (SRSWR) and
Simple random sampling without replacement (SRSWOR).

Concept of Point estimation. Requirement of good estimator: Unbiasedness, Consistency,
Efficiency. Elementary concept ofMVUE & BLUE.

Statistical tests of Hypothesis- Null & alternative hypothesis. Simple & composite
hypothesis, Critical region, Type-I and Type-II errors, Level of Significance and size of
critical region, Power of a test. Tests of significance related to a single BinomiaJ proportion,
Poisson parameter and ywo binomial proportions using large sample approximations. Exact
tests of hypothesis under normal set-up for a single mean, equality of two means and single
variance. Frequency Chi-square test & Goodness of fit.

N.B. : Theory Syllabus of Pre-test examination is aJso included in Test examination.

Unit wise Question Types with Marks Distribution of Test Examination (Theory)

Unjt Title of Unit MCQ/Objective SA-I SA-II LA Total
1 Mark 2Mark 3Mark SMark Marks
I Mathematics 3 2 I I 15
II Correlation & - I I I 10
Regression
Ul Probability & 2 I 2 2 20
Probability
Distributions
IV Sampling, 2 I 2 2 20
Estimation &
Testing of
Hypotheses
v Population Studies 3 l - - 05
TotaJ No. of Questions IO 6 6 6 -
Question wise Marks 10 12 18 30 70
distribution

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Practical Examination syllabus of Test Examination

Three experiments to be given in the examination as follows:

1. Sampling distribution and estimation of population mean and its standard error under
SRSWR and SRSWOR.

2. Large sample tests of a single mean, single proportion and difference. of two proportions.

3. Pearson' s Chi-square tests.

4. Exact tests of hypotheses under normal set-up for a single mean, difference of two means
and single variance.

5. Drawing of random sample from Uniform and Normal distributions

N.B. : Syllabus of Pre-test practical examination is also included in Test examination.

Marks Distribution of Test Examination (Practical)

Full Marks: 30, Time: 3 Hours

1. Experiments (5 + 5 + IO) 20 Marks

2. Practical Note Book (PNB) 5 Marks
3. Viva-Voce 5 Marks