Statistics

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09/09/2026

C. R. Rao (10 September 1920 – 22 August 2023)

Today marks his 106th birth anniversary.

A single 1945 paper, written at age 25, gave us the Cramér–Rao inequality (a lower bound on the variance of an unbiased estimator), the Rao–Blackwell theorem (variance reduction by conditioning on a sufficient statistic), and the treatment of Fisher information as a metric on parameter spaces, the origin of information geometry.

He also gave the score test (1948) and orthogonal arrays (1947), the latter underlying fractional factorial designs and Taguchi methods.

PhD at Cambridge under R. A. Fisher; four decades at the Indian Statistical Institute. Padma Vibhushan (2001), US National Medal of Science (2002), International Prize in Statistics (2023).

08/20/2026

A good dashboard is only as reliable as the data behind it. Missing values, duplicates, inconsistencies, and errors can easily produce misleading results.

Data cleaning is not a preliminary task, it is a necessary part of meaningful analysis and sound decision-making.

08/12/2026

Probability Distributions:
A probability distribution specifies how probability is allocated across the values a random variable can take. Once that allocation is fixed, the mean and variance follow from it, and so does any decision rule built on it.

This sheet covers the six distributions that carry most of an introductory course:

• Bernoulli: A single trial with two outcomes
• Binomial: Number of successes in n independent trials
• Poisson: Number of events in a fixed interval
• Geometric: Number of trials until the first success
• Uniform (continuous): All values in [a, b] equally likely
• Normal (continuous): The standard model for measurement and aggregated data

08/04/2026

Probability provides a systematic way to measure uncertainty and analyze the likelihood of events. This one-page concept note summarises the basic terms, event types, probability approaches, the addition and multiplication laws, conditional probability, and Bayes’ theorem. It may serve as a quick reference for students learning the foundations of probability.

07/29/2026

Skewness measures the direction and degree of asymmetry in a distribution. Positive skewness indicates a longer right tail, negative skewness indicates a longer left tail, and zero skewness suggests symmetry.

07/28/2026

Hypothesis testing helps us make decisions using sample data

07/27/2026

How the proportion of observations within a normal distribution changes as the z-score limit increases or decreases. A value beyond ∣z∣=2 may be treated as unusual, while ∣z∣≥3 is commonly used as a stronger criterion for identifying potential outliers.

07/12/2026

All models are wrong, but some are useful ~~George E. P. Box

07/02/2026

Life may never follow a normal distribution, but stand before your problems with the calm and balance of one ~ Sumit Maheshwari

06/29/2026

National Statistics Day 2026

India observes National Statistics Day on 29 June to commemorate the birth anniversary of Professor Prasanta Chandra Mahalanobis, whose work made a lasting contribution to statistics, large-scale sample surveys and economic planning in the country.

The theme for National Statistics Day 2026 is ‘Unlocking the Potential of Administrative Data.’ Administrative data are generated routinely through the functioning of government departments and public institutions. Records relating to education, health, taxation, employment, welfare programmes and public services can provide valuable evidence for planning and policy evaluation.

However, the availability of data alone does not ensure sound decision-making. Its usefulness depends on accuracy, completeness, consistency and timely updating. Data collected by different institutions must also be made interoperable and comparable. Clear standards for data integration, privacy, security and responsible access are therefore essential.

Administrative data should not be treated as a complete substitute for censuses, surveys or field-based research. Its value is greater when it is validated and combined with information from multiple sources. Such triangulation can improve the reliability and detail of official statistics while reducing duplication in data collection.

National Statistics Day reminds us that statistics is not merely a set of numerical techniques. It is a scientific basis for understanding social and economic conditions, evaluating public programmes and making decisions under uncertainty. Strengthening statistical capacity and data governance is therefore necessary for transparent, accountable and evidence-based administration.

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