Karnataka II PUC Statistics (KSEAB) study plan

Compute mean, median and mode for raw, discrete and continuous frequency distributions, including grouped data with open-end classes

Derive and apply the empirical relation between mean, median and mode, and locate the median and quartiles graphically from ogives

Calculate range, quartile deviation, mean deviation and standard deviation for grouped data and interpret what each measures

Compute coefficient of variation and use it to compare consistency between two data sets

Distinguish skewness from kurtosis and compute Karl Pearson's and Bowley's coefficients of skewness

Construct scatter diagrams and compute Karl Pearson's coefficient of correlation for grouped and ungrouped data

Compute Spearman's rank correlation, including the correction for tied ranks

Derive the two lines of regression from normal equations and use them to predict values and find the coefficient of determination

Define sample space, events and the three approaches to probability, and apply the addition and multiplication theorems

Solve conditional probability and Bayes' theorem problems set in real data-collection contexts

Distinguish discrete and continuous random variables, and derive probability mass and density functions from stated conditions

Compute expected value and variance of a random variable from its distribution and verify that total probability equals one

Fit a binomial distribution to given data by estimating p and q, and compute mean, variance and standard deviation of the fitted distribution

Fit a Poisson distribution using the estimated mean, and state the conditions under which Poisson is the limiting case of binomial

Use standard normal tables to find areas and solve problems converting to z-scores, including the normal approximation to binomial

Differentiate census from sample surveys and list the merits, limitations and appropriate use of each

Explain simple random sampling, stratified sampling and systematic sampling, and identify when each is preferred

State the central limit theorem and describe the shape, mean and standard error of the sampling distribution of the sample mean

Compute standard error of the mean with and without the finite population correction factor

Re-solve 10 previously missed central tendency and dispersion numericals under timed conditions

Classify data by nature and construct frequency distributions with correct class intervals, midpoints and inclusive-to-exclusive conversion

Build a less-than and a more-than cumulative frequency table from the same data and draw both ogives on one graph

Draw and label histograms, frequency polygons, frequency curves and pie charts, and read values from them

Compute Laspeyres, Paasche and Fisher's ideal index numbers and interpret the difference between them

Construct a cost of living index using the family budget method and apply the time and factor reversal tests to check a formula

Compute chain base index numbers and shift the base year of a given index series

Fit a straight line trend by the method of least squares to both odd and even numbers of years, and interpret the slope

Compute 3-yearly and 4-yearly moving averages and identify the trend from the smoothed series

Compute seasonal indices by the simple average method and explain the components of a time series

Estimate a trend value for a future year and state the assumptions that make the estimate valid

Define statistics in both singular and plural senses and state its scope and limitations in applied work

Distinguish primary from secondary data and list the merits and demerits of interviews, questionnaires and mailed surveys

Identify the types of scales of measurement and the errors that arise in data collection and tabulation

Design a short questionnaire and a tabulation plan for a stated survey objective

Outline the steps in a sample survey from objective definition to report writing

Assemble a one-page formula sheet spanning all ten domains and verify each formula by re-deriving it once

Complete two full-length timed mock papers under exam conditions and score them against the marking scheme

Review the error log from weeks 1-7 and re-solve every flagged problem until each is correct without notes

State the assumptions behind each theoretical distribution and each sampling method from memory

Identify the three highest-risk topics from mock performance and drill them to accuracy above 80 percent