Statistics for Business Analytics and Data Science A-Z™

Kick off with a beginner-friendly statistics primer covering continuous versus discrete variables, distributions, standard deviation, normal distribution, skewness, and mean, median, and mode, plus Cantor's diagonal argument and homework assignment.

Compare continuous and discrete variables with a bank customer dataset, illustrating real-valued versus categorical data, balance, age, regions, and age groups, and their impact on distributions.

Learn how mean, variance, and standard deviation describe data spread in a small population, using squared deviations from the mean to quantify dispersion and relate to mu and sigma.

Examine the normal distribution's bell-curve form, its probability density function, and how mu and sigma define the center and spread; learn key probabilities for standard deviation ranges.

Explore skewness in data distributions, identify left and right skew, and connect tails and outliers to the underlying data behind the chart.

Analyze mean, median, and mode, their behavior in left and right skewed distributions, and how outliers and duplicates influence calculations with the probability density function.

Create two 1000-observation normal distributions for US heights—men and women—and identify the 2.2% tallest cutoffs to test a high-end boutique sales forecast.

Learn to construct height distributions for men and women, compute means and standard deviations, determine the 2.2% cutoff, and create histograms in Excel.

Learn to build and update distributions for men and women using bins, the frequency function, and array formulas in Excel, illustrating how sampling affects mean, standard deviation, and charts.

Explore Cantor's diagonal argument and the continuum concept, proving that the real numbers between 0 and 1 are uncountable and form a stronger infinity than natural numbers.

Master the central limit theorem through intuition, populations and samples, and sampling distributions, and apply the z score to real-world business analytics challenges such as shipping in the US.

Define populations and samples, and explain how parameters describe entire populations while statistics describe samples. Explore why random sampling enables estimating population metrics with confidence and accuracy.

Explore the sampling distribution by repeatedly sampling a population, recording the sample means (X-bar), and plotting their distribution to prepare for the central limit theorem.

Apply the central limit theorem to see that the sampling distribution of the sample mean becomes normal, regardless of the population distribution, enabling practical insights in business analytics.

Understand central limit theorem intuition: the sampling distribution of the sample mean becomes normal, with a mean equal to the population mean and standard deviation that shrinks as n increases.

Explore the central limit theorem by visualizing the sampling distribution of the sample mean and observe how larger n yields a normal distribution with lower standard deviation.

Learn how the z score standardizes a normal distribution by centering at mu and scaling by sigma to estimate probabilities using the z table.

Apply the central limit theorem to a Fedex cargo scenario, using the sampling distribution of the mean for 36 boxes to estimate a 98.3 percent probability of safe takeoff.

Explore a Wall Street quant scenario modeling weekly profits with a Laplace distribution, mean $95.70 and standard deviation $1,247, using central limit theorem to estimate loss risk and $20,000 profit.

Explore how the central limit theorem shapes sampling distributions in a Wall Street homework problem, comparing mean profits, large standard deviation, and the probability of hitting targets or incurring losses.

Explore statistical significance and hypothesis testing with a live example and clear steps. Examine testing assumptions, intuition, pitfalls, region rejection approaches, and proportion testing, plus a homework exercise.

Explore statistical significance through intuition and hypothesis testing, using p-values and the null versus alternative hypothesis to decide when to reject the null.

Apply hypothesis testing to assess whether the millennials' tv viewing mean has decreased from 26.5 hours, using the null and alternative hypotheses, sampling distribution, z-score, and p-value.

Learn how to determine the rejection region in hypothesis testing using z scores and z critical values. Compare direct p-values with reverse-engineering 5% significance using a millennial TV viewing example.

Explore the assumptions behind the Z test and hypothesis testing, including random sampling, independence of observations, and knowing the population standard deviation or using a T test for smaller samples.

Test a proportion with a 97% significance level to see if tablet ownership exceeds 58% based on 100 households. Learn to compute p-hat, z-score, and p-value.

Evaluate a hypothesis test to prove defect reduction from 23% to under 18% with 95% confidence using a sample of 150 spoons.

Explore hypothesis testing with a spoon defect case, forming null and alternative hypotheses, using random samples, p-hat and z-score, and interpreting 95% confidence results.

Understand why you fail to reject the null hypothesis in hypothesis testing, using p-hat, z-scores, and 95% confidence to assess evidence against the alternative and guide experiment redesign.

Explore the t distribution, its heavier tails, and degrees of freedom, which adjust for small samples and unknown population standard deviation, converging toward normal distribution as degrees of freedom grow.

Execute a one-tailed t-test to infer if the population mean of daily steps is below 10,000, using x-bar, s, and nine degrees of freedom, with 95% confidence.

Explore the intuition behind one-tailed and two-tailed tests, including null and alternative hypotheses, rejection regions, and why two-tailed tests are stricter due to split significance.

Explore a two-tailed hypothesis test on a bookstore spending scenario, comparing a 57 baseline to a 62 sample mean, and apply z-scores, p-values, and central limit theorem logic.

Explore how misusing p-values can mislead research, and why reporting effect sizes and confidence intervals matters for understanding magnitude and practical significance in business analytics.

Explore how p values can mislead without revealing the magnitude of the effect, using a real world pharmacy example to guide cautious interpretation of hypothesis testing in business.

Celebrate completing this course with a personal thank you, featuring Tasmania scenery from Cradle Mountain to Crater Lake, and invite learners to rate and share feedback.