Statistics for Assistant Statistical Officer
The subject-specific paper tests statistical theory plus computation: central tendency and dispersion, moments, skewness and kurtosis, correlation and regression, probability distributions, sampling and estimation, hypothesis testing, index numbers, time series, vital statistics, and statistical quality control. Expect both definition-level and numerical questions.
Core rules
- Central tendency: mean uses every observation and is affected by outliers; median and mode are resistant. For a moderately skewed distribution the empirical relation is Mode ≈ 3 Median − 2 Mean.
- Dispersion: range, quartile deviation, mean deviation, and standard deviation. SD is the positive square root of variance, so it carries the same unit as the data.
- Correlation vs regression: r is unit-free and lies between −1 and 1; the regression coefficient b_yx = r·(σ_y/σ_x). Also b_yx·b_xy = r².
- Sampling: simple random, stratified, systematic, cluster; standard error decreases as √n increases.
- Index numbers: Laspeyres uses base-year quantities, Paasche uses current-year quantities; Fisher's ideal index is the geometric mean of the two.
Worked example
For a distribution, mean = 40 and median = 42. Using Mode = 3 Median − 2 Mean: Mode = 3(42) − 2(40) = 126 − 80 = 46. Note the assumption: the empirical relation holds only for moderately skewed distributions, not for strongly skewed data.
Traps that cost marks
- Mixing sample and population variance (dividing by n versus n − 1).
- Treating r² as correlation rather than the coefficient of determination.
- Assuming mean and median coincide in a skewed distribution.
- Using Laspeyres and Paasche quantities interchangeably.