Sunflower Intelligence
Business Analytics & Data Science

B04 · Intermediate

Descriptive and Inferential Statistics

10 lessons

B04 · Intermediate · 10 lessons in four modules · about 13.5 hours

Descriptive and Inferential Statistics

Describe data and chance, then reason from samples to populations with confidence intervals, tests for means and proportions, chi-square tests and ANOVA, by hand and in Excel.

What you will learn

  • Describe a distribution’s centre, spread, position and shape with measures suited to the data, and say which resist outliers and skew.
  • Calculate and interpret probabilities from contingency tables, using conditional probability, independence and Bayes’ rule.
  • Model counts with the binomial and Poisson distributions and measurements with the normal distribution, and check whether a model fits.
  • Explain sampling distributions and the central limit theorem, and calculate and interpret standard errors.
  • Construct and interpret confidence intervals for means and proportions, and plan the sample size a margin of error needs.
  • Carry out and report hypothesis tests for means and proportions (one and two samples, paired), with p-values, Type I and Type II errors and power.
  • Test relationships between categorical variables with chi-square tests, compare several group means with one-way ANOVA, and check each test’s conditions.
  • Report results with intervals and effect sizes, separate statistical from practical significance, allow for multiple comparisons, and say what the evidence can’t show (non-response, self-selection, causation).

Prerequisites

How it works

Each lesson teaches the idea from first principles, works examples step by step, lets you explore it in an interactive, then has you practise with feedback. A lesson is complete when you have worked its guided problems and scored 80% on its knowledge check. Mastery is tracked separately and comes back for review before you are likely to forget. Each module ends with a test; the course ends with a project and a final assessment.

Fictional case

Lantern Coffee Co. A fictional coffee business founded by Ana Lim. It starts as a catering and barista-training service, opens its own cafés and an online shop for beans, and plans a canned cold brew. Every name and figure in it is invented for teaching.

Not sure where to start?

The diagnostic has 12 questions across the course. It doesn’t count toward anything; it suggests the module to start from. Take the diagnostic.

Modules and lessons

Module 1 Describing data and chance

  1. Describing distributionsBefore you infer anything from data, describe it exactly: its centre, its spread, where a value sits within it and its shape. Learn the notation that separates a population from a sample, why the sample variance divides by n − 1, what z-scores, percentile ranks and the coefficient of variation say, and when the empirical rule or only Chebyshev’s inequality applies.75 min · not started
  2. ProbabilityProbability is the language every test and interval in this course is written in. Learn to read joint, marginal and conditional probabilities from a contingency table, to use the addition and multiplication rules, to check whether two events are independent, to draw a tree diagram, and to turn a screen’s accuracy into the probability that a flagged case is real with Bayes’ rule.70 min · not started
  3. Discrete distributionsMany business questions are about counts: subscriptions among the next orders, orders on a day, boxes sold at a market. Learn to describe a count with a probability distribution, its expected value and its standard deviation, to recognise the binomial and Poisson distributions and check their conditions, and to calculate their probabilities by hand and with BINOM.DIST and POISSON.DIST.75 min · not started
  4. Module 1 test12 questions on this module. 70% passes.not taken

Module 2 From samples to populations

  1. The normal distributionModel a measurement with the normal curve: turn values into z-scores, find the share of bags under a label weight and the machine setting that keeps it below 1%, with NORM.DIST and NORM.INV and by hand. Then check whether the model fits, and see where it fails.85 min · not started
  2. Sampling distributionsA sample’s mean or proportion changes from one sample to the next. See how much, through the standard error σ ÷ √n and the central limit theorem, on Lantern’s strongly skewed spring orders; use the normal model for a sample mean, and know when it misleads. Then compare the ways of drawing a sample and the biases that no sample size cures.80 min · not started
  3. Confidence intervalsTurn a sample’s mean or proportion into a range for the population’s, with a margin of error that says how far it could be off. Build z and t intervals for a mean and an interval for a proportion, by hand and with CONFIDENCE.NORM and CONFIDENCE.T; say exactly what “95% confident” means; and work out the sample a margin needs.85 min · not started
  4. Module 2 test12 questions on this module. 70% passes.not taken

Module 3 Testing hypotheses

  1. Hypothesis testingTurn a business worry into a null and an alternative hypothesis, measure how surprising the data would be if nothing were wrong, and decide with a p-value or a critical value. Test Kilnworth’s 1 kg bags with a z test and a t test and September’s conversion against its target, then weigh Type I and Type II errors, power, practical significance and the traps of running many tests.85 min · not started
  2. Comparing two meansCompare two means the way the data were collected: with a paired t test when the same units are measured twice, and with Welch’s t test when the groups are separate. Run both by hand, with T.TEST and with the Analysis ToolPak, put an interval and an effect size on the difference, and check the conditions before trusting any of it.80 min · not started
  3. Module 3 test12 questions on this module. 70% passes.not taken

Module 4 Categories and groups

  1. Proportions and chi-square testsCompare two proportions with a z test and a confidence interval, then use the chi-square distribution to test whether counts fit a model and whether two categorical variables are related. Calculate each test by hand and in Excel with CHISQ.TEST, CHISQ.DIST.RT and CHISQ.INV.RT, check its conditions, and say what a result does and doesn’t show.90 min · not started
  2. One-way analysis of variance (ANOVA)Compare the means of several groups at once without inflating the chance of a false alarm. Split variation into between- and within-group parts, build the F statistic by hand and with Excel’s Anova: Single Factor, check the conditions, measure the effect with η², and find which groups differ with adjusted comparisons.85 min · not started
  3. Module 4 test11 questions on this module. 70% passes.not taken

Project and final assessment

  1. Project: Lantern’s evidence reviewWeigh the evidence behind four of Ana’s decisions for 2027: a courier trial, the gift-box email test, workshop formats and a subscriber survey; plan the 2027 customer survey; and write her a memo that separates what the data show from what they don’t.not taken
  2. Final assessment24 questions across the whole course. 70% passes.not taken

The course is complete when every lesson is complete, every module test is passed, the project is finished and the final assessment is passed.

Resources

  • Glossary: every term this course defines.
  • Formulas: every formula with its symbols and units.
  • Review: flashcards and the questions you missed, when they are due.

Elsewhere on this site

Sources used in this course

  1. Holmes, A., Illowsky, B. & Dean, S. (2023). Introductory Business Statistics 2e, section 2.7, “Measures of the Spread of the Data” (n − 1, Chebyshev’s rule, the empirical rule, the coefficient of variation, z-scores). OpenStax. openstax.org/books/introductory-business-statistics-2e/pages…
  2. Microsoft Support. “TRIMMEAN function”, with the pages for DEVSQ and STANDARDIZE. support.microsoft.com/en-us/office/trimmean-function-d90c987…
  3. Microsoft Support. “PERCENTRANK.INC function”. support.microsoft.com/en-us/office/percentrank-inc-function-…
  4. Microsoft Support. “KURT function”, with the page for SKEW. support.microsoft.com/en-us/office/kurt-function-bc3a265c-5d…
  5. Westfall, P. H. (2014). “Kurtosis as Peakedness, 1905–2014. R.I.P.” The American Statistician, 68(3), 191–195. doi:10.1080/00031305.2014.917055. ideas.repec.org/a/taf/amstat/v68y2014i3p191-195.html
  6. Ault, S. V., Liao, S. N. & Musolino, L. (2025). Principles of Data Science, section 3.4, “Probability Theory” (Bayes’ theorem and a screening example). OpenStax. openstax.org/books/principles-data-science/pages/3-4-probabi…
  7. Microsoft Support. “COMBIN function”, with the page for PERMUT. support.microsoft.com/en-us/office/combin-function-12a3f276-…
  8. Illowsky, B. & Dean, S. (2023). Introductory Statistics 2e, section 4.2, “Mean or Expected Value and Standard Deviation”. OpenStax. openstax.org/books/introductory-statistics-2e/pages/4-2-mean…
  9. Microsoft Support. “BINOM.DIST function”, with the pages for BINOM.DIST.RANGE, POISSON.DIST and EXPON.DIST. support.microsoft.com/en-us/excel/functions/binom-dist-funct…
  10. NIST/SEMATECH. e-Handbook of Statistical Methods, sections 1.3.6.6.18, “Binomial Distribution”, and 1.3.6.6.19, “Poisson Distribution”. itl.nist.gov/div898/handbook/eda/section3/eda366j.htm
  11. NIST/SEMATECH. e-Handbook of Statistical Methods, section 1.3.6.6.1, “Normal Distribution”. itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
  12. NIST/SEMATECH. e-Handbook of Statistical Methods, section 1.3.3.21, “Normal Probability Plot”. itl.nist.gov/div898/handbook/eda/section3/normprpl.htm
  13. Microsoft Support. “NORM.DIST function”, with the pages for NORM.S.DIST, NORM.INV, NORM.S.INV and STANDARDIZE. support.microsoft.com/en-US/Excel/functions/norm-dist-functi…
  14. Microsoft Support. “NORMDIST function” and “NORMSDIST function” (replaced by NORM.DIST and NORM.S.DIST; kept for backward compatibility). support.microsoft.com/en-US/excel/functions/normdist-functio…
  15. Holmes, A., Illowsky, B. & Dean, S. Introductory Business Statistics, section 7.1 “The Central Limit Theorem for Sample Means”. OpenStax. openstax.org/books/introductory-business-statistics/pages/7-…
  16. OpenStax Introductory Business Statistics, section 1.2 “Data, Sampling, and Variation in Data and Sampling”, on Statistics LibreTexts. stats.libretexts.org/Bookshelves/Applied_Statistics/Business…
  17. Kott, P. S. & Levine, B. (2024). “Exploring a skewness conjecture: Expanding Cochran’s rule to a proportion estimated from a complex sample”. Survey Methodology 50(2), 543–551. Statistics Canada. www150.statcan.gc.ca/n1/pub/12-001-x/2024002/article/00001-e…
  18. Microsoft Support. “RAND function”, with the page for SKEW.P (the skewness of a whole population). support.microsoft.com/excel/functions/rand-function
  19. NIST/SEMATECH. e-Handbook of Statistical Methods, section 1.3.5.2, “Confidence Limits for the Mean”. itl.nist.gov/div898/handbook/eda/section3/eda352.htm
  20. Illowsky, B. & Dean, S. Introductory Statistics, section 8.3 “A Population Proportion” (np′ and nq′ both greater than 5; sample size with p′ = 0.5). OpenStax. openstax.org/books/introductory-statistics/pages/8-3-a-popul…
  21. Diez, D., Barr, C. & Çetinkaya-Rundel, M. OpenIntro Statistics, section 6.1 “Inference for a Single Proportion”, on Statistics LibreTexts. stats.libretexts.org/Bookshelves/Introductory_Statistics/Ope…
  22. Agresti, A. & Coull, B. A. (2001). Comment on “Interval Estimation for a Binomial Proportion”. Statistical Science 16(2), 117–120. users.stat.ufl.edu/~aa/articles/agresti_coull_2001.pdf
  23. Microsoft Support. “CONFIDENCE.T function”, with the pages for CONFIDENCE.NORM, T.INV.2T, T.INV and T.DIST.2T. support.microsoft.com/en-US/Excel/functions/confidence-t-fun…
  24. Wasserstein, R. L. & Lazar, N. A. (2016). “The ASA’s statement on p-values: context, process, and purpose”. The American Statistician, 70(2), 129–133. doi.org/10.1080/00031305.2016.1154108
  25. Microsoft Support. “Z.TEST function”. support.microsoft.com/en-US/excel/functions/z-test-function
  26. Microsoft Support. “T.DIST function”. support.microsoft.com/en-US/excel/functions/t-dist-function
  27. Microsoft Support. “T.DIST.2T function”. support.microsoft.com/en-US/excel/functions/t-dist-2t-functi…
  28. Microsoft Support. “T.INV.2T function”. support.microsoft.com/en-US/excel/functions/t-inv-2t-functio…
  29. NIST/SEMATECH. e-Handbook of Statistical Methods, sections 7.2.2, “Are the data consistent with the assumed process mean?”, and 7.2.2.2, “Sample sizes required”. itl.nist.gov/div898/handbook/prc/section2/prc222.htm
  30. Microsoft Support. “T.TEST function”. support.microsoft.com/en-US/excel/functions/t-test-function
  31. Microsoft Support. “Use the Analysis ToolPak to perform complex data analysis” (the t-Test and F-Test Two-Sample for Variances tools). support.microsoft.com/en-us/excel/use-the-analysis-toolpak-t…
  32. Microsoft Support. “F.TEST function”. support.microsoft.com/en-US/excel/functions/f-test-function
  33. NIST/SEMATECH. e-Handbook of Statistical Methods, section 1.3.5.3, “Two-Sample t-Test for Equal Means”. itl.nist.gov/div898/handbook/eda/section3/eda353.htm
  34. Delacre, M., Lakens, D. & Leys, C. (2017). “Why psychologists should by default use Welch’s t-test instead of Student’s t-test”. International Review of Social Psychology, 30(1), 92–101. doi.org/10.5334/irsp.82
  35. Illowsky, B. & Dean, S. Introductory Statistics 2e, section 13.4, “Test of Two Variances”. OpenStax. openstax.org/books/introductory-statistics-2e/pages/13-4-tes…
  36. Holmes, A., Illowsky, B. & Dean, S. (2017). Introductory Business Statistics, section 10.4, “Comparing Two Independent Population Proportions”. OpenStax. openstax.org/books/introductory-business-statistics/pages/10…
  37. NIST/SEMATECH. e-Handbook of Statistical Methods, section 1.3.5.15, “Chi-Square Goodness-of-Fit Test”. itl.nist.gov/div898/handbook/eda/section3/eda35f.htm
  38. Microsoft Support. “CHISQ.TEST function”, with the pages for CHISQ.DIST.RT and CHISQ.INV.RT. support.microsoft.com/en-us/excel/chisq-test-function
  39. Weisstein, E. W. “Cramér’s V”. MathWorld, a Wolfram Resource. mathworld.wolfram.com/CramersV.html
  40. NIST/SEMATECH. e-Handbook of Statistical Methods, section 1.3.6.6.5, “F Distribution”. itl.nist.gov/div898/handbook/eda/section3/eda3665.htm
  41. NIST/SEMATECH. e-Handbook of Statistical Methods, section 7.4.7, “How can we make multiple comparisons?”, with 7.4.7.3, “Bonferroni’s method”. itl.nist.gov/div898/handbook/prc/section4/prc47.htm
  42. Penn State Eberly College of Science. STAT 500 Applied Statistics, section 10.2.1, “ANOVA Assumptions”. online.stat.psu.edu/stat500/book/export/html/607
  43. Microsoft Support. “F.DIST.RT function” and “F.INV.RT function”. support.microsoft.com/en-us/excel/functions/f-dist-rt-functi…
  44. Delacre, M., Leys, C., Mora, Y. L. & Lakens, D. (2019). Taking parametric assumptions seriously: arguments for the use of Welch’s F-test instead of the classical F-test in one-way ANOVA. International Review of Social Psychology, 32(1). doaj.org/article/258fa30b5d304f3d9900c7b6b93b37f9