Statistics & Probability
The subject that decides whether a claim is evidence or noise, taught on real data from the first week.
Flexible course duration
Duration depends on the student's background and pace. Beginners (kids / teens): typically 6 to 9 months. Adults with prior knowledge: often shorter, with an accelerated path.
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Program Overview
Statistics is the working mathematics of almost every field that touches data: business, medicine, psychology, economics, engineering, machine learning. It is also routinely taught backwards, as formula memorisation first and meaning never. This 6-month live course teaches it the other way. Months 1 and 2 build the two foundations: describing data honestly, and probability as the grammar of uncertainty, including conditional probability and Bayes' theorem worked through real cases like medical test results. Months 3 and 4 cover the distributions that model the world, then sampling, the central limit theorem seen through simulation rather than assertion, and confidence intervals interpreted the way they actually work. Month 5 is hypothesis testing done properly: t-tests, proportion tests and chi-square, with equal attention to what p-values do not say. Month 6 covers correlation and regression, then a capstone: a full analysis of a real dataset of your choosing, written up with methods and limitations.
Every technique is practised on real data in a spreadsheet, and an optional Python track runs alongside for those who want it. Neither is required knowledge coming in; one of them becomes a working skill going out.
What Makes This Program Different
- Real datasets from week 1: public health, sports, economics and business data, not textbook tables invented to make the arithmetic clean
- Spreadsheet-first with an optional Python track, so non-programmers finish everything and programmers get the pandas version of each technique
- Probability taught through consequential examples: false positives in medical testing, base-rate mistakes, and why intuition fails on conditional probability
- The central limit theorem demonstrated by simulation you run yourself, because a theorem you have watched happen is one you actually trust
- Honest inference: what a p-value is and is not, why statistical significance is not importance, and how p-hacking happens
- A capstone analysis of a dataset you choose, written up with methods and limitations like a piece of real analytical work
Your Learning Journey
Career Progression
Detailed Course Curriculum
Explore the complete week-by-week breakdown of what you'll learn in this comprehensive program.
Topics Covered
- Populations, samples and why the difference drives everything
- Types of data: categorical and numerical, and the scales of measurement
- Tidy data: rows, columns and the shape analysis expects
- Where data comes from: surveys, experiments, logs and their built-in biases
- Spreadsheet setup: importing, cleaning basics and first summaries
- Famous data failures: survivorship bias and selection bias with real stories
Projects You Build
- First dataset walk: load a real public dataset, document its variables, units and suspicious values before computing anything
Practice & Assignments
Profile two provided datasets: identify variable types, spot three data-quality problems, write one paragraph on each
Topics Covered
- Mean, median and mode, and what question each one answers
- How skew and outliers pull the mean away from the median
- Weighted means and when unweighted averages mislead
- Group comparisons: the danger of comparing averages of unequal groups
- Computing summaries in the spreadsheet with named functions
- Reading claims critically: what average salary headlines usually hide
Projects You Build
- Income exercise: a salary dataset summarised with mean and median, with a written note on why they disagree and which to report
Practice & Assignments
12 central tendency problems on real data, each answer accompanied by one sentence on which measure fits and why
Topics Covered
- Range and interquartile range
- Variance and standard deviation, built up from deviations rather than dropped as a formula
- The 1.5 IQR rule for flagging outliers
- z-scores: how unusual is this value
- Comparing variability across different units with the coefficient of variation
- Why spread is the half of the story that dashboards leave out
Projects You Build
- Consistency study: two players or products with the same average compared on spread, with a recommendation written up
Practice & Assignments
14 spread problems including 4 z-score questions, standard deviation computed once by hand and thereafter by software
Topics Covered
- Histograms and the shapes of distributions: symmetric, skewed, bimodal
- Box plots and comparing groups at a glance
- Scatter plots and the first look at relationships
- Bar charts versus histograms, and why the difference matters
- Misleading charts: truncated axes, cherry-picked windows, area distortions
- Building clean charts in the spreadsheet, with labels that earn their space
Projects You Build
- Chart audit: find one misleading chart in the wild, explain the distortion, and rebuild it honestly from the underlying data
Practice & Assignments
Build five charts from a real dataset, each with a one-line takeaway written underneath
Assessment
Month 1 checkpoint: a full descriptive analysis of a provided dataset, summaries, charts and a short written brief
Topics Covered
- Experiments, outcomes, sample spaces and events
- Probability as long-run frequency and as degree of belief
- The complement rule and the addition rule
- Mutually exclusive events versus events that overlap
- Venn diagrams that actually resolve arguments
- Simulating simple probabilities in the spreadsheet to check intuition
Projects You Build
- Simulation warm-up: estimate a dice probability by simulation, compare with the exact answer, watch the gap shrink with more trials
Practice & Assignments
16 probability problems from single events to unions, each hard one checked by a quick simulation
Topics Covered
- Conditional probability: how information changes the odds
- The multiplication rule and tree diagrams
- Independence: what it means and how to test for it
- The base-rate fallacy introduced with a real screening example
- Sampling with and without replacement
- Why P(A given B) and P(B given A) are different, and the famous confusions
Projects You Build
- Two-way table study: a real dataset cross-tabulated, with conditional probabilities read off and independence checked
Practice & Assignments
14 conditional probability problems, every tree diagram drawn before any multiplication
Topics Covered
- Bayes' theorem derived from the definition of conditional probability
- The medical test problem: why a positive result on a rare disease is usually a false alarm
- Prior, likelihood and posterior in plain language
- Natural frequencies: the counting method that makes Bayes intuitive
- Spam filters and diagnostic reasoning as everyday Bayes
- The prosecutor's fallacy and other courtroom probability errors
Projects You Build
- Bayes explainer: work the medical test problem with natural frequencies and write an explanation a friend could follow
Practice & Assignments
10 Bayes problems solved twice each, once by formula and once by counting, until the two views agree in your head
Topics Covered
- Permutations and combinations, and which one the question wants
- Discrete random variables and probability distributions
- Expected value: what fair means, and why casinos always win
- Variance of a random variable
- Expected value in decisions: insurance, warranties and lotteries
- Building a probability distribution from real frequency data
Projects You Build
- Game analysis: compute the expected value of a real lottery or carnival game and write the verdict in two sentences
Practice & Assignments
12 counting and random variable problems including 3 expected-value decisions argued in writing
Assessment
Month 2 checkpoint: a mixed probability paper from basic rules through Bayes and expected value
Topics Covered
- Bernoulli trials and the binomial conditions, checked in words
- The binomial formula and where it comes from
- Mean and variance of a binomial
- Computing binomial probabilities in the spreadsheet and, on the Python track, with scipy
- Cumulative probabilities and careful at-least versus at-most reading
- Real binomial settings: quality control, conversion rates, free-throw streaks
Projects You Build
- Conversion study: model a marketing conversion scenario as a binomial and answer three business questions with it
Practice & Assignments
14 binomial problems, the conditions checked in writing before any computation
Topics Covered
- The Poisson distribution for counts per interval: arrivals, defects, calls
- When Poisson fits and when it does not
- Poisson as a limit of the binomial, seen numerically
- The geometric distribution: waiting for the first success
- Choosing the right model: binomial, Poisson or geometric from the story
- Fitting a Poisson to real count data and judging the fit by eye
Projects You Build
- Arrivals study: fit a Poisson model to real count data, compare observed and expected counts in a table
Practice & Assignments
12 modelling problems where the first marked step is naming the right distribution and defending the choice
Topics Covered
- From histograms to density curves: probability as area
- The uniform distribution as the simplest continuous case
- The normal distribution: shape, parameters and the 68-95-99.7 rule
- Standardising and the standard normal
- Normal probabilities by software, with the table method understood once
- What is and is not normal in real data: heights yes, incomes no
Projects You Build
- Normal check: test the 68-95-99.7 rule against a real dataset and report where it holds and where it breaks
Practice & Assignments
14 normal distribution problems, each one opened with a sketch of the shaded region
Topics Covered
- Inverse problems: finding cutoffs from probabilities
- Percentiles, reference ranges and grading on a curve
- Assessing normality with histograms and quantile plots
- The normal approximation to the binomial and when it is safe
- Combining independent normal quantities
- A distribution field guide: one page mapping situations to models
Projects You Build
- Field guide build: your own one-page reference mapping real situations to binomial, Poisson, geometric, uniform or normal
Practice & Assignments
12 mixed distribution problems where the model is never announced in the question
Assessment
Month 3 checkpoint: a distributions paper mixing model choice, computation and interpretation
Topics Covered
- Simple random, stratified, cluster and systematic sampling
- Convenience samples and why most internet polls mean little
- Sampling bias, nonresponse bias and question wording effects
- Famous polling failures and what went wrong
- Randomised experiments versus observational studies
- Designing a small survey that will not embarrass you
Projects You Build
- Survey critique: take one published poll, identify its sampling method, and write three specific bias risks
Practice & Assignments
10 sampling design problems plus one short survey designed, with its weaknesses honestly listed
Topics Covered
- The sampling distribution of the mean: a distribution of statistics, not data
- Standard error and why bigger samples pin the mean down
- The central limit theorem stated carefully
- The CLT demonstrated by simulation: skewed populations, normal-looking sample means
- How sample size affects the shape, watched live
- Why the CLT is the load-bearing wall of everything that follows
Projects You Build
- CLT simulation: run the resampling experiment yourself in the spreadsheet or Python, and keep the charts as evidence
Practice & Assignments
10 standard error and sampling distribution problems, plus the simulation repeated on a second population shape
Topics Covered
- The logic of interval estimation
- z-intervals and t-intervals, and when the t-distribution is the honest choice
- Degrees of freedom in plain language
- What 95 percent confidence actually means, and the misreadings to avoid
- Interval width: the three levers of confidence, spread and sample size
- Computing and reporting intervals from real data
Projects You Build
- Interval report: a confidence interval for a real dataset's mean, reported in one correct sentence and one wrong-but-common sentence, labelled
Practice & Assignments
12 confidence interval problems, every interval followed by a correctly worded interpretation
Topics Covered
- Confidence intervals for proportions
- Margin of error and how polls report it
- Sample size calculations: how many people do we actually need
- Reading polling small print: confidence level, margin, population
- Intervals for differences, previewed
- Estimation recap: the full toolkit so far, organised
Projects You Build
- Poll deconstruction: take a real published poll and verify its stated margin of error from its sample size
Practice & Assignments
12 proportion and sample size problems including two taken from real published surveys
Assessment
Month 4 checkpoint: an estimation paper from sampling design through confidence intervals, interpretation marked as strictly as computation
Topics Covered
- Null and alternative hypotheses: the courtroom analogy done carefully
- Test statistics and the p-value defined precisely
- Significance levels and the arbitrary honesty of 0.05
- Type I and Type II errors, and which one your situation fears more
- What a p-value is not: not the probability the null is true
- One-tailed versus two-tailed tests and how to choose before seeing data
Projects You Build
- Error analysis: for three real scenarios, name both error types and argue which is costlier in each
Practice & Assignments
10 test-logic problems with no computation at all: hypotheses, tails and error types only
Topics Covered
- The one-sample t-test for a mean, start to finish
- The one-sample proportion test
- Checking conditions before trusting the test
- Computing tests in the spreadsheet and, on the Python track, with scipy
- Writing conclusions in context, with the p-value reported not worshipped
- Confidence intervals and tests as two views of the same evidence
Projects You Build
- Claim check: test a real advertised claim against real or provided data, and write the verdict in three sentences
Practice & Assignments
12 one-sample tests, each conclusion written in context and checked against its confidence interval
Topics Covered
- Independent two-sample t-tests
- Paired tests and recognising paired designs
- Two-proportion tests: the A/B test in its natural form
- Effect size: statistically significant versus actually important
- How A/B testing works in product teams, and where it goes wrong
- Reading a published study's methods section without fear
Projects You Build
- A/B analysis: a realistic conversion dataset analysed end to end, with a recommendation that weighs effect size, not just p
Practice & Assignments
12 two-group problems including one paired design hiding among independent ones
Topics Covered
- Chi-square goodness of fit: does the data match the claimed distribution
- Chi-square test of independence on two-way tables
- Expected counts and when the test is valid
- Multiple comparisons: why testing twenty things finds one false discovery
- p-hacking and publication bias: how honest people fool themselves
- Pre-registering your question: deciding what to test before looking
Projects You Build
- Independence study: a real two-way table tested for independence with the full expected-count working shown
Practice & Assignments
10 chi-square problems plus a written half-page on one real p-hacking case
Assessment
Month 5 checkpoint: a full inference paper across one-sample, two-sample and chi-square tests, conclusions marked for wording
Topics Covered
- Covariance and the Pearson correlation coefficient
- What r measures and the linear-only caveat
- Anscombe's quartet: four datasets, one r, four different stories
- Correlation is not causation, with the confounder named each time
- Rank correlation for curved but monotonic relationships
- Computing and charting correlations across a real dataset
Projects You Build
- Correlation hunt: find the three strongest relationships in a real dataset, chart them, and flag which might be confounded
Practice & Assignments
10 correlation problems, every claim of relationship backed by a scatter plot
Topics Covered
- The least squares line: what is being minimised and why
- Interpreting slope and intercept in the units of the problem
- R-squared: how much variation the line explains
- Residual plots: the honesty check most analyses skip
- Prediction within range versus extrapolation beyond it
- Multiple regression previewed: several predictors at once, and its dangers
Projects You Build
- Prediction model: fit a regression on real data, check residuals, make two predictions and state their limits
Practice & Assignments
10 regression problems with slope interpretations written in context every time
Assessment
Capstone gate: analysis plan approved, dataset, question, methods and chosen track (spreadsheet or Python)
Topics Covered
- Framing an answerable question before touching the data
- Cleaning and documenting the dataset
- Choosing methods that fit the data, not the other way around
- Descriptive pass first: summaries and charts before any test
- Running the inference or regression the question calls for
- Instructor review checkpoint mid-build
Projects You Build
- Capstone analysis in progress: the full pipeline from raw data to preliminary findings, on your own chosen dataset
Practice & Assignments
Capstone work sessions with a written progress note after each: what was found, what is uncertain, what is next
Topics Covered
- Structuring an analysis report: question, data, methods, findings, limitations
- Writing limitations honestly: what your analysis cannot claim
- Charts chosen for the reader, not the author
- Presenting analytical work in ten minutes
- Answering methods questions about your own work
- Where to go next: deeper statistics, Python for data, or machine learning
Projects You Build
- Completed capstone: a written analysis report and a short presentation, delivered to the class and kept for your portfolio
Practice & Assignments
Final report polish plus a dry-run presentation with peer questions
Assessment
Capstone review: report and presentation assessed on method, honesty of interpretation and clarity, plus certificate review
Projects You'll Build
Build a professional portfolio with A portfolio of small real-data studies plus one complete capstone analysis with report and presentation real-world projects.
Weekly Learning Structure
Certification & Recognition
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Support & Resources
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Transform your career with industry-ready skills and job placement support.
Prerequisites
Who Is This Course For?
Career Paths After Completion
Salary & Market Context
The ranges below are general market salary bands for roles where statistics is a core skill, in India and abroad, drawn from public industry data. They are shown for career context only and are not a promise or guarantee of income. Actual pay depends on your skills, experience, location, and the job market.
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