Tamil Nadu HSE First Year Statistics study guide
Tamil Nadu HSE First Year Statistics · Work through your exam, one topic at a time.
The Tamil Nadu Higher Secondary First Year Statistics course is the Class 11 (+1) statistics subject offered under the state higher secondary curriculum. It suits students who have chosen the statistics stream and want a quantitative foundation before Class 12, and it is also useful for anyone building early skills in data handling, summarising data and basic inference. The Tamil Nadu HSE First Year Statistics study guide has 9 sections and about 2,034 words.
01Scope of Statistics and Data Collection
Statistics is the science of collecting, organising, presenting, analysing and interpreting data. The exam tests the scope of statistics and the distinction between primary and secondary data, plus the main collection methods.
301 words, about 2 min02Measures of Central Tendency
Arithmetic mean = Σx/n; for grouped data use midpoints and frequencies, or assumed mean and step-deviation methods. Median is the middle value; for grouped data, median = l + ((n/2 − cf)/f)h.
238 words, about 1 min03Measures of Dispersion
Range = L − S; coefficient of range = (L−S)/(L+S). Quartile deviation QD = (Q3−Q1)/2; coefficient = (Q3−Q1)/(Q3+Q1).
208 words, about 1 min04Skewness and Kurtosis
Skewness measures asymmetry. Symmetric: mean = median = mode; positive or right skew: mean median mode; negative or left skew: mean < median < mode.
209 words, about 1 min05Correlation and Regression
Karl Pearson r = Σ(x−x̄)(y−ȳ) / √[Σ(x−x̄)² Σ(y−ȳ)²]; it lies between −1 and 1 and is unit-free. r 0 means a positive linear relation; r < 0 negative; r = 0 means no linear relation.
236 words, about 1 min06Probability
Sample space S lists all outcomes; event A is a subset. 0 ≤ P(A) ≤ 1 and P(S) = 1.
197 words, under 1 min07Random Variables and Mathematical Expectation
A discrete random variable takes countable values with probability mass function p(x), where Σp(x) = 1. A continuous random variable has density f(x) ≥ 0 with total area 1; P(X = a) = 0 for any single point.
205 words, about 1 min08Sampling Techniques and Sampling Distributions
Probability sampling includes simple random (with or without replacement), stratified, systematic, cluster and multistage sampling. Non-probability sampling includes convenience, quota and purposive or judgement sampling.
230 words, about 1 min09Index Numbers
An index number measures relative change from a base period, usually with base = 100. Simple aggregate index = (Σp1/Σp0)×100.
210 words, about 1 min