Data Science & Analytics Mathematics

Statistics & Probability

The subject that decides whether a claim is evidence or noise, taught on real data from the first week.

6 months (24 weeks) College students and working professionals; no programming required 2 live classes/week + 3-4 hours practice Course-completion certificate from Modern Age Coders
Statistics & Probability: Data to Hypothesis Testing

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.

Standard pace6 to 9 months
AcceleratedAdd class frequency to finish faster

For personalised duration planning, call +91 91233 66161 and we'll map a schedule to your goals.

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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

Phase 1
Foundations: describing data with the right summaries and charts, then probability, conditional probability, Bayes' theorem and random variables
Phase 2
Models and estimation: binomial, Poisson and normal distributions, sampling and the central limit theorem, and confidence intervals done honestly
Phase 3
Inference and the capstone: hypothesis tests for means, proportions and categories, correlation and regression, then a full real-data analysis of your own

Career Progression

1
The statistical core that analyst roles and graduate courses assume
2
The ability to read a study, a dashboard or an A/B test result and know what it does and does not show
3
Working fluency in spreadsheet analysis, plus optional Python with pandas for those who take that track
4
A completed capstone analysis you can show: question, method, findings and limitations
5
The prerequisite base for machine learning and data science courses, where statistics is the half people arrive missing

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.

A full descriptive analysis brief on a real public dataset
A Bayes explainer of the medical test problem in your own words
An expected-value verdict on a real lottery or game
A Poisson model fitted to real count data
A CLT simulation run and charted by you
A deconstruction of a real published poll's margin of error
An A/B test analysed end to end with an effect-size-aware recommendation
A regression prediction model with residual checks
The capstone a complete written analysis of a dataset you chose

Weekly Learning Structure

Live Classes
2 live one-hour classes per week, working on real data during class
Practice
3-4 hours weekly of problem sets and dataset work between classes
Review
Homework reviewed with written feedback; interpretation wording corrected as strictly as calculations

Certification & Recognition

Completion
Course-completion certificate from Modern Age Coders, backed by your capstone analysis report

Technologies & Skills You'll Master

Comprehensive coverage of the entire modern web development stack.

Describing data honestly with the right summaries and charts
Probability, conditional probability and Bayes' theorem used correctly
Choosing and applying binomial, Poisson and normal models
Confidence intervals and hypothesis tests, computed and worded properly
Correlation and regression with the honesty checks included
Spreadsheet analysis throughout, plus optional Python with pandas and scipy on the parallel track

Support & Resources

Doubt Support
WhatsApp doubt support between classes, with worked solutions for stuck problems
Progress Updates
Monthly progress notes covering test scores and capstone readiness
Career Guidance
Honest guidance on next steps: which roles use these skills, what to learn next, and what this course alone does and does not qualify you for

Career Outcomes & Opportunities

Transform your career with industry-ready skills and job placement support.

Prerequisites

Maths Level
Comfortable school algebra: rearranging formulas and working with fractions and percentages. No calculus is needed anywhere in the course
Programming
None. Everything can be completed in a spreadsheet; the Python track is optional and taught from zero for those who choose it
Equipment
A computer with a spreadsheet application (Excel or Google Sheets) and a stable internet connection
Audience
Built for college students and working professionals; motivated final-year school students who clear the diagnostic are welcome

Who Is This Course For?

College Students
Students in commerce, economics, psychology, biology or engineering whose degrees assume statistics that was never properly taught
Working Professionals
Analysts, marketers, product managers and operations people who face dashboards and A/B tests daily and want to stop nodding along
Data Science Aspirants
People headed for data science or machine learning who know the statistics half is the half they are missing
Researchers
Postgraduate students and early researchers who need to design studies and read papers with methods sections
Non Programmers
Anyone who wants rigorous data skills without being forced through a programming course to get them

Career Paths After Completion

Data analyst and reporting analyst roles, where descriptive statistics and inference are the daily toolkit
Business and product analytics: A/B testing, metrics and experiment literacy
A prepared entry into data science and machine learning courses, including our Python and AI/ML tracks
Research work in any field with a methods section: psychology, economics, public health
Better decisions in your current role, which is the quiet majority use of statistics

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.

Early Career Roles
₹3-6 LPA (Data Analyst / Reporting Analyst / MIS Analyst)
Growing Roles
₹6-12 LPA (Senior Analyst / Business Analyst / Product Analyst)
Experienced Roles
₹12-25 LPA (Analytics Lead / Data Scientist, typically with added programming and ML skills)
International
$55k-110k USD (USA) for analyst roles, depending on role, industry and experience

Course Guarantees

Live Classes
Live, interactive classes with a real instructor, never pre-recorded videos.
Small Batches
Small batches only: group classes are capped at 10 students, with mini-batch (3 to 4 students) and personal 1-on-1 options.
Structured Curriculum
A structured, well-paced curriculum taught step by step, with hands-on practice in every session.
Doubt Support
Doubt support between classes over WhatsApp, so you are never left stuck.
Certificate
A course-completion certificate you can share.
Free Demo
A free demo class before you enrol, so you can decide with no pressure.

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