Kerala Plus Two Statistics (DHSE) study plan

Construct frequency distributions (inclusive/exclusive) and cumulative frequency tables from raw data, and compute relative frequencies.

Draw and interpret histograms, frequency polygons, ogives, and box plots for given datasets.

Calculate mean, median, mode, and quartiles for raw and grouped data, including weighted mean.

Compute range, quartile deviation, mean deviation, and standard deviation for raw and grouped data.

Explain the effect of change of origin and scale on dispersion measures and coefficients.

Derive and apply the combined mean and combined variance formulas for two groups.

Compute Karl Pearson's and Spearman's rank correlation coefficients and interpret their signs and magnitudes.

Fit a simple linear regression line using least squares and interpret slope and intercept.

Calculate the coefficient of determination and explain its meaning in context.

Distinguish between correlation and regression, and identify properties (range, units, symmetry).

Define sample space, events, and axioms of probability; compute probabilities for classical and relative frequency setups.

Apply addition theorem, multiplication theorem, and conditional probability formulas to solve problems.

Use Bayes' theorem to compute posterior probabilities in two-stage experiments (e.g., disease testing, urn models).

Construct tree diagrams for multi-stage experiments and verify results using the theorem.

Solve problems on independence and mutually exclusive events, avoiding common fallacies.

Define discrete and continuous random variables and construct their probability distributions.

Compute expected value, variance, and standard deviation of a random variable from its distribution.

Find the distribution of a function of a random variable (e.g., Y = aX + b) and verify properties of expectation.

Calculate probabilities using the cumulative distribution function (CDF) for discrete and continuous cases.

Apply expectation and variance to real-life decision problems (e.g., expected profit).

State the conditions for a binomial distribution and compute probabilities using the formula and tables.

Calculate mean and variance of a binomial distribution and solve word problems.

State the conditions for a Poisson distribution and compute probabilities, including the Poisson approximation to the binomial.

Fit binomial and Poisson distributions to given frequency data and test goodness of fit conceptually.

Solve problems involving the relationship between binomial and Poisson distributions.

Distinguish between population and sample, and between parameter and statistic.

Explain sampling methods (SRSWR, SRSWOR, stratified, systematic) and their advantages/limitations.

Derive the sampling distribution of the sample mean for normal populations and apply the central limit theorem.

Compute standard error of the mean and proportion, and interpret it.

Solve problems on sampling distribution of mean and proportion for small and large samples.

Distinguish between point and interval estimation, and compute confidence intervals for mean (large sample and t-distribution) and proportion.

State null and alternative hypotheses, and differentiate Type I and Type II errors.

Perform one-sample and two-sample tests for means (large sample Z-test, small sample t-test) and for proportions.

Conduct chi-square goodness-of-fit and independence tests, and interpret p-values.

Explain the concept of power of a test and factors affecting it.

Review all formula sheets and create a master formula booklet for quick reference.

Solve at least two full-length practice papers under timed conditions (3 hours each).

Analyze mistakes from practice papers and re-solve incorrect problems.

Revise weak areas identified from practice tests, focusing on high-weight domains (1, 2, 4).

Practice previous years' questions (if available) and verify answers with textbook solutions.