WBCHSE Class 11 Syllabus 2024 Statistics

WEST BENGAL COUNCIL OF HIGHER SECONDARY EDUCATION
SYLLABUS FOR CLASSES XI AND XII

COURSE OVERVIEW :
Nowadays , Statistics has become an indispensible subject in every sphere of life, specially in the fields of
Engineering, Commerce, Industry, Agriculture, Bio-Technology , Education , Economics, Physical Science and
Social Science.

Sincere attempt has been taken in including the topics in Class XI and Class XII, so that students are familiarized
with the content and ideas of those topics.

This Higher Secondary Statistics Syllabus included all the topics covered by the leading boards of India in HS
level. Utmost care has been taken in selecting and preparing the topics for both the classes. Most of the topics
will help HS students in their All India Entrance Examinations and Entrance tests of the reputed Institutions. Not
only that, the students who are willing to pursue their studies in basic sciences will also get immense help.

For some advance topics, only a few salient features have been discussed to give the students a brief idea.

CLASS - XI
SEMESTER – I
FULL MARKS: 35 CONTACT HOURS: 60 Hours
COURSE CODE : THEORY

UNIT No. TOPICS CONTACT HOURS MARKS
UNIT 1 Introduction: Meaning of statistics, Nature of 03 02
statistics, Importance of statistics, Relation with
some allied subjects, Uses of statistics, Misuses of
statistics
Types of data: Primary and Secondary data, 06 04
Quantitative data and Qualitative data, Discrete
data and continuous data, Time series , Spatial
series data and cross-sectional data, ordinal data
and nominal data, Illustration with examples
UNIT 2 Collection of data: Questionnaire and its basic 05 01
characteristics, Definition of Schedule and pilot
survey, Designing a questionnaire and schedule,
concept of outliers.
Scrutiny of data: Checking internal consistency and 04 02
detection of error in collection and in recording.
UNIT 3 Presentation of data: Textual representation, Tabular 09 04
representation, Diagrammatic representation (line
diagram, Multiple axes diagram and multiple line
diagram), Bar diagram (Horizontal and vertical bar
diagrams, multiple and divided bar diagrams), Pie
diagram
UNIT 4 Frequency distribution, Cumulative frequency 09 05
distribution and their graphical representation
(Column diagram, Step diagram, ogive, Histogram,
frequency curve of different types, Stem and leaf
diagram)
UNIT 5 Official Statistics: Structure and activities of some 04 03
organizations (NSSO, CSO, DGCSIR, Labour
Borough, Agricultural Statistics, MOSPI)
UNIT 6 Concept of Central Tendency and its measures with 13 09
properties including AM≥GM≥HM.
UNIT 7 Index No.: Definition of Index Number, Types of 07 05
Index No.(Price Index, Quantity Index, Value Index),
Construction of Price Index No. and its uses, Various
Price Index formulae(Laspeyres', Paasche's,
Edgeworth-Marshall and Fisher), Tests of consistency
(Time reversal test and Factor reversal test)
TOTAL 60 Hours 35

CLASS - XI
SEMESTER – II
FULL MARKS: 35 CONTACT HOURS: 40 Hours
COURSE CODE : THEORY
UNIT No. TOPICS CONTACT HOURS MARKS
Measures of Dispersion: Range, Mean deviation, 10 10
UNIT 1 Standard deviation, Quartile deviation, Coefficient of
variation, Quantile and Percentile
with relation between different measures
Raw and central moments up to fourth order and 07 06
their conversions Cauchy –Schwartz Inequality
UNIT 2 Measures of Skewness and Kurtosis: Different
measures based on moments and
quantities(associated inequalities involving 𝑏1 and 𝑏2
coefficients)
Random experiment: Sample Space, Notion of events 12 12
and operations with events.
Definition of Probability: Classical and Relative
frequency approach to probability with limitations.
UNIT 3 Axiomatic Definition of Probability (Statement only)
Theorem of Total Probability, Bonferroni’s
inequality, Boole’s inequality.
Compound Probability, Conditional Probability and
Bayes’ theorem, Statistical Independence of events
(No. of events not more than three) and related
problems.
Concept of polynomials, Different forms of n-th 05 03
degree polynomials relating to two different
interpolation formulae, Remainder theorem.
UNIT 4 Concept of Interpolation, ∆ and E operators and their
relation.
Simple Interpolation : Newton’s Forward and
Backward Interpolation
formulae (without Derivation)
Population Statistics: 06 04
Introduction: Vital events, Sources of data on Vital
events, Rates and Ratio of vital events.
UNIT 5 Measurement of Mortality: CDR,SDR,STDR
Measurement of Fertility: CBR,GFR,ASFR,TFR
Measurement of Population Growth: Crude rate of
Natural increase and Vital index.
TOTAL 40 Hours 35

[Note:20 Hours reserved for Remedial classes, Tutorials and Home Assignments.]

CLASS - XII
SEMESTER – III
FULL MARKS: 35 CONTACT HOURS: 60 Hours
COURSE CODE : THEORY

UNIT No. TOPICS CONTACT HOURS MARKS

UNIT 1 Mathematics: 16 06
Concept of series and sequence, Concept of
convergence and divergence and related sums.
Infinite series, e-series and log series and related
sums. Concept of Maximum and Minimum, Concept
of Partial derivative, Concept of Infinite
Integral(Gamma integral and Beta integral and their
relation with factorial)
UNIT 2 Probability Distributions 15 10
Random Variables and its Probability distribution,
Cumulative distribution function, Probability Mass
Function, Probability density function , Expectation,
Variance
UNIT 3 Some Discrete Distribution 16 12
Uniform distribution, Binomial distribution, Poisson
distribution, Geometric distribution and their
properties with related problem Sums. Fitting of
above distributions.
UNIT 4 Least square method and curve fitting (linear and 04 02
exponential)
UNIT 5 Time series Analysis 09 05
Introduction, Different components of time series,
Different models of time series, Trend
determination by method of simple moving
averages and by fitting Mathematical curves
(straight line and exponential curve)using least
square principle.
TOTAL 60 Hours 35

CLASS - XII
SEMESTER – IV
FULL MARKS: 35 CONTACT HOURS: 40 Hours
COURSE CODE : THEORY
UNIT No. TOPICS CONTACT HOURS MARKS

Descriptive Statistics: 09 10

UNIT 1 Bivariate Data, Scatter diagram, Two - way
frequency distribution, Marginal and conditional
distribution. Simple correlation and its properties.

Simple regression Analysis and its related results

Rank data and rank correlation.(Spearman’s Rank
Correlation coefficient –case of no tie)

Some Continuous Distribution 07 07

Rectangular distribution and Normal distribution.
their properties with related problem Sums. Fitting
UNIT 2
of above distributions.

Sampling theory and Sampling distribution 06 05

Population and Sample, Parameter and Statistic,
Complete Enumeration and sample surveys, Basic
principles of sample survey, Advantages of Sample
survey over complete enumeration. Concept of
UNIT 3 probability sampling, Practical methods of drawing
a random sample using a random Number Table,
SRSWR and SRSWOR, Concept of Sampling
distribution of sample mean and its standard error.

p.d.f and shape of χ2 , t and F with expectation and 03 02
variance
UNIT 4
(without derivation)

Estimation 05 03

Idea of inference, Point estimation, Interval
estimation, Estimator and estimate. Four basic
criteria of Estimator, Concept of bias. Idea of
UNIT 5 unbiasedness and minimum variance unbiasedness.
Point estimation of Binomial proportion, Poisson
mean ,normal mean and variance (using method of
moments).

Testing of Hypothesis: 06 05
Statistical test of Hypothesis-Null and Alternative
hypothesis, Simple and Composite Hypothesis,
Type I and Type II error, Critical region, level of
significance, Power of a test, One sided and Two
sided tests. Critical Value.
UNIT 6
Tests of significance related to a single Binomial
Proportion and Poisson Mean(using Large sample
approximation), Mean and Variance of a single
univariate Normal distribution.

Statistical Quality Control 04 03
Introduction, Idea of Quality and Quality Control,
Advantages of Statistical Quality Control, Process
UNIT 7
and Lot control, Control chart technique.
Construction of control charts by variables (𝑋 𝑅)
and attributes(p, np)

TOTAL 40 Hours 35

[Note:20 Hours reserved for Remedial classes, Tutorials and Home Assignments.]

CLASS: XI
COURSE CODE: PRACTICAL
FULL MARKS: 30 CONTACT HOURS: 80
PROBLEMS FOR PRACTICAL EXAMINATION: 18 (5×2+4×2)
LABORATORY NOTE BOOK : 04, PROJECT WORKS : 05, VIVA-VOCE : 03

List of Problem Sets :

1. Tabular Presentation of Data, Scrutiny of Data
2. Diagrammatic Representation of Data (Non-Frequency Type)
3. Construction of Frequency Distribution and Graphical Representation of them (Univariate Data only, both
Discrete and Continuous Variables)
4. Calculations Relating to Measures of Central Tendency (Problems involving Open Ended Classes, Missing
Frequencies, Pooling of Two Sets of Data, Checking Empirical Relations, Finding Median Graphically using
Ogives, Finding Mode using Histogram, Checking the Correctness of the Measures etc.)
5. Calculations Relating to Measures of Dispersion (Problems involving Open Ended Classes, Missing Frequencies,
Pooling of Two Sets of Data, Step Deviation Methods using shift of Origin and/or Change of Scale, Checking the
correctness of the Measures etc.)
6. Calculations Relating to Moments and Measures of Skewness and Kurtosis
(Comment on the Nature of Frequency Distribution, Verification of the Inequalities
involving 𝑏 and 𝑏 is desirable)
7. Problems involving Polynomial, ∆-Operator, Finite Difference Table etc.
8. Calculations Relating to Index Numbers and their tests
9. Calculations Relating to Mortality Rates and Fertility Rates
10. Project Works: It will be based on Descriptive Statistics.
Here, we propose some mini-projects :
(a) Prepare a questionnaire for collecting data on age-sex composition of different families of the locality of a
student.
(b) Collect data on age, family size, place of residence (Urban/Rural) and religion of all the students of your
class or other class. Construct frequency distribution of all the variables and represent them by suitable
diagrams.
(c) Collect data on height and weight of all the students of your class or other class. Construct frequency
distribution of all the variables and represent them by suitable diagrams.
(d) Collect the maximum daily temperature (°C) and minimum daily temperature (°C) of your city from
weather report for consecutive 30 days. Then compare these two distributions using suitable diagrams.
(e) Collect data on the percentage of marks obtained in the last public examination of all the students of your
class and present the data using suitable diagrams.
(f) Collect data on height/weight of a group of students. Calculate the different measures of Central
Tendency. Comment on the nature of data (skewness) based on the result you obtained.

CLASS: XII
COURSE CODE: PRACTICAL
FULL MARKS: 30 CONTACT HOURS: 80
PROBLEMS FOR PRACTICAL EXAMINATION: 18 (5×2+4×2)
LABORATORY NOTE BOOK : 04, PROJECT WORKS : 05, VIVA-VOCE : 03
List of Problem Sets :

1. Scatter Diagram, Calculation of Correlation Coefficient and Regression Coefficient, Identifying the Regression
Equations, Finding the Regression Equations from Bivariate Data, Problems on Spearman’s Rank Correlation
Coefficient (case of no tie).

2. Application and Fitting of Binomial, Poisson and Normal Distributions.

3. Drawing of Random Samples in SRSWR and SRSWOR using Random Number Tables.

4. Sampling Distribution of Sample Mean from a Finite Population based on SRSWR and SRSWOR (Start with a
population having a finite number of values (4, 5, 6 etc.); choose a sample size of 2, 3 etc.; list all possible
samples of the chosen size; calculate sample mean based on each such sample; obtain the sampling distribution
of the sample mean and display this distribution diagrammatically).

5. Estimation of Population Mean and Standard Error of the Estimator of Population Mean under SRSWR and
SRSWOR.

6. Testing of Hypothesis in case of Poisson Parameter, Mean and Variance of Normal Distribution, 𝜒 goodness of
fit.

7. Determination of Trend in Time Series Data using Moving Average Method (period of moving average even and
odd), Linear trend equation and Exponential trend equation.

8. Construction of Control Chart (p, np, 𝑥̅ , R)

9. Project Works :

Here, we propose some mini-projects :

(a) Collect the marks obtained in Test Examination and in Final Examination in MP for the students of a year.
Plot the data to obtain a scatter diagram showing the relation between these two sets of scores. Calculate
Correlation Coefficient and also obtain the Regression Lines. Estimate Final score based on Test score for
the students. Compare estimated scores and actual scores. Are they same? If not, then what is the
interpretation of it? Explain this in the conclusion of your project report.

(b) Collect data on heights (in inches) and weights (in kg) of a group of students of same gender and same age
group. Draw the scatter diagram of these bivariate data. Calculate correlation coefficient and then
compute the regression equations of both the types.

(c) Collect data on age of father and mother of a group of your friends. Rank the data. Using ranked data,
calculate Rank Correlation Coefficient. Comment on the result you obtained.

(d) Collect the maximum daily temperature (°C) and minimum daily temperature (°C) of your city from
weather report for consecutive 30 days. Then plot the data using a suitable scale. Comment on the nature
of the data you obtained.

(e) Purchase 10 different chocolates from a nearby shop. Ask your two friends separately to rank them
according to their preference. Using these data, check whether their preferences are related or not.

(f) From a group of students of a class select a sample of size 10 using Random Number Table by SRSWR and
SRSWOR. Estimate sample mean and sample variance based on the result you obtained.

(g) Collect the data on the movement of BSE SENSEX for last two weeks. Fit a linear trend to the data and
calculate the predicted value for next two days. Verify the correctness of the predicted values with the
actual values. Comment on the result you obtained.

INSTRUCTIONS for Laboratory Session and

Preparation of Laboratory Note Book for STATISTICS.

1. For Laboratory Note Book, square sheets and white sheets both are to be used by the students, but if the
square sheets are not available then the students may use Laboratory Note Book as used in practical of
Biological Sciences, Physics and Chemistry etc.

2. Strictly, HB pencil is to be used in laboratory sessions. Scientific calculators (Non-Programmable) may be used. If
required, Statistical Tables are to be supplied by the institutions. Geometry Box may also be used.

3. A problem set on a specific topic covering different numerical problems based on Secondary data is to be
supplied to the students in a laboratory session. This may be typed or printed or neatly hand-written in white
papers.

Each problem set should carry at the top

(a) The problem set number

(b) Heading (in capital letters)

(c) Working date

4. While solving any problem in any of the problem sets, students must mention the necessary theory along with
relevant formula and notations, in brief, wherever and whenever needed in the square sheets. No derivation or
discussion is needed. Use tables for showing the calculations.

5. The necessary calculations are to be shown stepwise with specification of units, wherever required. Calculations
should be presented neatly, whenever required, in a square sheet or in the ruled side of the inter-leaf sheet.

6. For graphs and diagrams the cm/mm graph papers are to be used. Both the axes should be labelled clearly,
scales to be mentioned and the name of the charts/ diagrams are to be mentioned clearly. The graph sheets are
to be presented adjacent to the relevant calculations of the problems concerned.

7. All the problem sets enlisted in the syllabus must be completed, examined and signed with date by the teacher
concerned. Finally, it should be arranged serially according to the content index.

8. There should be a content index at the very beginning of the Laboratory Note Book which consists of

(a) Serial Number of the Chapters

(b) Heading of the Chapters

(c) Working Date

(d) Running Page Number

RULES for the Practical Examination

1. The Practical Examination is to be held on a single date simultaneously in all the institutions.

2. If it is not possible to hold the examination on a single date, then there should be at least three sets of
questions for different dates since Statistics Practical is a numerical problem based practical.

3. The Practical Examination will be of two hours duration including Viva-Voce.

4. Questions of Viva-Voce may be asked by the External Examiner to test the depth and understanding of the
student in both theory and practical, preferably on Project Work.

5. Only non-programmable scientific calculators are allowed in the examination.

6. Statistical table will not be given in the question paper. Only some required values will be given in the question
paper. Statistical tables, if required, should be supplied by the institutions on the date of examination for
consultation of the students.

7. The completed Laboratory Note Book duly checked covering all the topics/chapters as prescribed in the
syllabus must be submitted during the Practical Examination of both Class XI and Class XII.

8. Students must bring the completed Project Work given to them on the date of Practical Examination.