Tamil Nadu HSE First Year Statistics study plan

Define statistics in the singular and plural sense, and list three functions and two limitations of statistics in your own words

Classify the following as nominal, ordinal, interval or ratio data: exam marks, blood group, ranking in a race, temperature in Celsius

Compute the arithmetic mean for raw data, a discrete frequency distribution and a grouped frequency distribution with class intervals, showing the step-deviation shortcut

Distinguish between a census and a sample survey, and state two situations where a sample survey is preferable

Compute the median and mode for raw data and for a grouped frequency distribution, using the standard interpolation formula for each

Compute the geometric mean and harmonic mean for raw data and state one practical situation where each is preferred to the arithmetic mean

Locate the median and quartiles graphically using an ogive drawn from a cumulative frequency table

Derive the empirical relation among mean, median and mode for a moderately skewed distribution and apply it to find a missing value

Solve for a missing frequency when the mean of a grouped distribution is given

Compare the merits and demerits of mean, median and mode, and choose the appropriate average for a stated real-life context

Compute range, quartile deviation and its coefficient for raw data and for a grouped frequency distribution

Compute mean deviation about the mean and about the median for raw and grouped data, and state which is smaller and why

Compute variance and standard deviation using the direct, assumed-mean and step-deviation methods, and verify that all three give the same answer for one data set

Compute the coefficient of variation for two data sets and decide which is more consistent

Explain why standard deviation is preferred to range and quartile deviation as a measure of dispersion

Draw a scatter diagram for a given bivariate data set and describe the direction and strength of the relationship

Compute Karl Pearson's coefficient of correlation for raw data and for a grouped frequency distribution

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

Interpret a computed correlation coefficient, and explain with an example why correlation does not imply causation

Derive the two lines of regression from the normal equations and compute the regression coefficients byx and bxy

State the properties of the correlation coefficient, including its limits, its symmetry, and its independence of change of origin and scale

Use the relation between regression coefficients and the correlation coefficient to recover a missing value

Define skewness and distinguish between positive and negative skewness using a frequency curve sketch

Compute Karl Pearson's and Bowley's coefficients of skewness for a grouped distribution

Define kurtosis, distinguish leptokurtic, mesokurtic and platykurtic curves, and compute the moments-based measure for a simple data set

State the classical, relative-frequency and axiomatic definitions of probability, and give one limitation of each

Apply the addition theorem for two and three events, including the mutually exclusive and exhaustive cases

Apply the multiplication theorem for independent events and for conditional probability, and use Bayes' theorem on a two-stage problem

Solve problems using permutations and combinations, including arrangements with repeated items

Compute the probability of at least one success and use the complement rule to simplify a counting problem

Distinguish between a discrete and a continuous random variable, and construct a probability distribution for a stated experiment

Compute the mean, variance and standard deviation of a discrete random variable from its probability mass function

State the properties of the binomial distribution, and compute probabilities, mean and variance for a stated n and p

Compare simple random sampling, stratified sampling and systematic sampling, and state one advantage and one limitation of each

State the central limit theorem and explain the standard error of the sample mean, including how it changes with sample size

Distinguish between a price relative and a link relative, and construct a simple aggregative price index

Compute Laspeyres', Paasche's and Fisher's ideal index numbers from a given price and quantity table

Interpret the time reversal and factor reversal tests, and check whether Fisher's ideal index satisfies both

Compute the cost of living index using the weighted aggregate method, and explain the limitations of index numbers

Complete two full-length timed practice papers under exam conditions and classify every error as conceptual, computational or careless