CHSE Odisha Elective Statistics study plan

Compute mean, median, mode, geometric mean and harmonic mean for raw, discrete and grouped data, and state which average is appropriate for a given data type

Calculate quartile deviation, mean deviation, variance and standard deviation for grouped data using both direct and assumed-mean (shortcut) methods

Derive and apply the relations among standard deviation, variance and coefficient of variation, and compare consistency of two data sets using CV

Compute and interpret moments (raw and central) up to the fourth order, and check skewness and kurtosis from them

State the axioms of probability and prove the addition theorem for two and three events, plus the multiplication theorem for independent events

Apply conditional probability and Bayes' theorem to solve classification-style problems with two or three events in the partition

Define discrete and continuous random variables, construct their probability mass and density functions, and verify the total probability equals 1

Derive the expectation and variance of a function of a random variable, and use the linearity of expectation on composite variables

Compute the moment generating function for simple discrete distributions and use it to obtain mean and variance

Derive the mean, variance and MGF of the binomial distribution, and fit a binomial distribution to a given frequency table

Derive the mean and variance of the Poisson distribution, and apply it as a limit of the binomial and to queuing/counting problems

Solve problems on the geometric and negative binomial distributions, distinguishing clearly when each applies

Derive the mean and variance of the continuous uniform and exponential distributions, and compute interval probabilities for each

State the normal distribution's density, standardise values via z-scores, and use standard normal tables for forward and inverse problems

Compute Karl Pearson's and Spearman's rank correlation coefficients, and interpret sign and magnitude in context

Fit lines of regression of y on x and x on y using least squares, and verify that the product of the two regression coefficients equals r squared

Distinguish a population, sample, parameter and statistic, and enumerate the principal steps and merits of sampling versus complete enumeration

Compare simple random sampling, stratified sampling and systematic sampling, and compute the standard error of the sample mean under SRS with and without replacement

State the central limit theorem and explain why the sampling distribution of the mean approaches normality as n grows

Distinguish null and alternative hypotheses, one-tailed versus two-tailed tests, and define Type I error, Type II error and power

Construct a large-sample test for a single mean and for the difference of two means, and state the decision rule in terms of the critical value

Apply the Student's t-test for a single mean, difference of two means and paired samples, choosing the correct degrees of freedom

Perform a chi-square test of goodness of fit and of independence in a contingency table, and state the assumptions

Carry out an F-test for equality of two variances and interpret the p-value against a chosen significance level

State the principles of replication, randomisation and local control, and explain how each reduces experimental error

Set up the one-way ANOVA model, compute between-group and within-group sums of squares, and complete an ANOVA table

Test the equality of several means using the F-statistic and interpret the result in the language of the experiment

Describe the layout of a completely randomised design and a randomised block design, and identify when blocking is appropriate

Derive the expected mean squares for a one-way classification and explain the role of the degrees of freedom

Compute moving averages of order 3, 4 and 5, and explain which order removes which periodicity

Fit a linear trend by the least squares method and by the method of semi-averages, and forecast two periods ahead

Compute seasonal indices using the ratio-to-moving-average method and verify that the indices sum to 400 for quarterly data

Construct Laspeyres, Paasche and Fisher's ideal index numbers, and verify the time reversal and factor reversal tests

Explain the chain base method, splicing of index series and the concept of a cost-of-living index

Revise every formula sheet from weeks 1 to 7 and rebuild a single condensed master sheet from memory

Complete two full-length timed mock papers under exam conditions, allocating time per mark value

Re-solve every problem previously marked wrong, without looking at the original solution, and log the recurring error types

Drill the highest-weight domains (1, 3, 4, 6) with 10 rapid numerical questions each until accuracy exceeds 85%

Rehearse the derivations most likely to be asked as proofs: binomial and Poisson mean and variance, sampling distribution of the mean, and the one-way ANOVA table