Curriculum And Syllabus For Classes XI & XII

STATISTICS

CLASS XI

One Paper

 3 Hours

100 Marks

Units

1.

 Mathematical Preliminaries

20 Marks 30 Periods

Set Theory-Theory of sets; set operation (union and intersection) and complementary of sets. Venndiagram, De-Morgan’s laws ; Permutations and combinations (basic concepts only), Binomial theorem with positiveintegral index, logarithms, Exponential series. Concept of function. Limit, Differentiation, Partial differentiation involving 3 ( three ) Variables,Maxima and Minima.

2.

 Descriptive Statistics

  25 Marks 30 Periods

Measures of dispersion, skewness and kurtosis and their coefficients ( up to 4th order only ). Moments raw and central moments and their relationship, cumulants, Moment generating function, characteristic function.

3.

 Association and Contingency

15 Marks 30 Periods

Concept of attribute, class and class frequency, positive, negative and independence of association, coefficient of association and contingency.

4.

 Index Numbers

20 Marks 35 Periods

Elementary theory of index numbers, steps in the construction of price index numbers and their uses. Construction of index numbers- Laspeyre’s Paasche’s and Fisher's ideal index numbers. Time reversal test and factor reversal test for the consistency of an index number, chain index number. Cost of living index number.

5.

 Time Series

5Marks 8 Periods

Time series and its components, Measurement of trend by moving average method.

6.

Vital Statistics

15 Marks  27 Periods

Meaning of Vital Statistics, Measurement of mortality rates-CDR, SPDR, STDRand CBR ; Measurement of fertility and reproduction rates ; Construction of complete life-table.

Books Recommended

  1. College Algebra by Das and Mukherjee.

  2. Elementary Statistics by H.C. Saxena, (S. Chand &Co)

  3. Differential Calculus by Das and Mukherjee.

STATISTICS

Class XII

One Paper

 3 Hours

100 Marks

Units

1.

Probability and Expectations

25 Marks 35 Periods

Event-Simple and compound ; sample space, Mathematical, Statistical and set theoretic definitions of probability ; Additive and Multiplicative laws of probability ; Random variables, Expectation of discrete random variable; Theorems on expectations of sun, and product of random variables.

2.

 Calculus of Finite Differences

15 Marks 20Periods

Delta ( ∆ ) and E operators and their properties ; construction of difference tables,  Newton's forward and backward interpolation formulae, Lagrange's interpolation formula.

3.

 Numerical Integration

10 Marks 10 Periods

Derivation of General quadrature formula, Trapezoidal rule, Simpson's 1/3rd and 3/8th rules.

4.

 Method of Least Squares and Curve Fitting

5 Marks 10 Periods

Methods of least squares, Fitting of straight lines and exponential curves by the method of least squares.

5.

 Correlation and Regression  (Bivariate only)

 15 Marks 30 Periods

Scatter diagram, Lines of regression ; Correlation co-efficient, Invariant property and Limits of correlation coefficient, Regression co-efficient, Relation between regression coefficients and correlation co-efficient Angle between the lines of regression.

6.

Standard Distributions

10 Marks  10 Periods

Binomial distribution and Poisson distribution ( with derivation) ; Normal distribution (without derivation).

7.

 Test of Significance

  10 Marks 10 Periods

Level of significance and concept of degrees of freedom; Test of significance for small samples based on t, X 2 and F.

8.

 Sample Survey

10 Marks 15 Periods

Random numbers' table ; Drawing of samples using random numbers table; Simple random sampling.

Books Recommended

  1. Elementary Statistics by H.C. Saxena, (S. Chand & Co.)

  2. Calculus of Finite Difference by H.C. Saxena.

  3. Fundamentals of Statistics ( Vol. 1 & 11 ) by Goon, Gupta and Das Gupta.