The Comprehensive Data Analyst Course.

Learn sql basics using an online sql workbench to practice queries on real tables, such as customer, category, employee, order details, and product.

Execute a select statement to read and display all information from a table, noting that star means everything and using top five rows for quick data insight.

Use the limit command in SQL to view a subset of rows from tables like orders or customers, quickly revealing columns and data types to understand a dataset.

Learn how to perform column filtering in SQL by selecting specific columns, such as postal code and country, and using limit to restrict rows.

Master the distinct command in sql by returning unique city and country combinations and ordering by city and country to reveal non-redundant, structured data.

master SQL querying by using where clauses to filter rows, select specific columns, order results, and apply distinct to reveal unique values in product data.

Learn how to use aggregate functions like count, min, max, sum, and average on a table such as order details to compute totals, minima, maxima, and averages across all rows.

Learn how to use the group by command to count customers by city, apply aggregate functions such as sum, min, max, and average, rename columns, and order and limit results.

Master the and, or, and null conditions in sql by combining filters with between, greater than, and less than, and handling missing data with is null and is not null.

Explore the like operator and wildcard characters, including percent sign (zero or more characters) and underscore (one character), to find Maria in the customers table for the course.

Explore left, right, inner, and full outer joins, plus self joins, and learn how to connect order details and products with on clauses.

Explore left and right joins to preserve data, selectively select columns with table stars, and join orders with employees to show order details and product names.

Explains inner, left, and full outer joins with practical examples, showing how matches, nulls, and duplicates arise; introduces self joins to pair customers by city.

Learn how to use the in command to filter customers by multiple cities and countries, such as Berlin, Germany, France, and the UK, in a single query.

Learn how the having clause, used after where and after group by, filters aggregated results like country counts, and why having is an elegant, optimized alternative.

Master the union command to append results from two queries, ensuring identical column structure and matching column names.

Master the any and all sql commands with subqueries to filter products by related order details, understand why subqueries return a single column, and manage duplicates.

Statistics answer questions with data and distinguish population from sample. Describe data with mean, median, and mode, and contrast descriptive and inferential statistics to inform decisions and predict outcomes.

Explore the definition of a random variable as an unknown value outcome from experiments, with discrete and continuous examples like dice faces and rain indicators.

Explore eight data types for random variables—discrete and continuous, categorical and numerical, nominal and ordinal, qualitative and quantitative—through practical examples like name, gender, age, percentile, ratings, and pin codes.

Explore central tendency concepts—mean, median, and mode—and learn when to use each. Understand ordinal versus nominal data and how outliers influence interpretations.

Explore central tendency with real examples, showing mode for categorical data like states or grades, and when mean or median apply based on nominal versus ordinal data and ordering.

Explore data visualization by differentiating categorical and numerical data, and present insights with bar charts, pie charts, and histograms, including frequency and cumulative frequency, mean, median, and mode.

Explore percentile, range, and quartiles, and learn to identify the median (50th percentile), the lower and upper quartiles (25th and 75th), and the interquartile range.

Explore how to compute and interpret quartiles and the interquartile range from data, and visualize them with a box plot; compare mean, median, and mode, and understand skewness.

Explore how standard deviation and variance quantify data spread around the mean, compare population and sample formulas, and apply the coefficient of variation to assess variability.

Explain why sample standard deviation uses n minus one, not n, and how using the sample mean instead of the population mean biases the sample variance.

Explore covariance and correlation between two variables, identifying positive or negative relationships, and learn to compute correlation as covariance divided by the product of standard deviations.

Explore the normal (gaussian) distribution, its properties, and how to standardize it into a unit normal via z-scores, linking to chi-square distribution.

Explore the chi square distribution, the sum of squares of k independent standard normal variables, with degrees of freedom guiding its shape and table-based probabilities for categorical associations.

Examine how the chi square distribution tests goodness of fit by comparing observed and expected frequencies under a null hypothesis, and compute the chi square statistic and degrees of freedom.

Explore how the chi-square distribution tests the association between two categorical variables, comparing observed and expected values, formulating null and alternative hypotheses, and interpreting results with degrees of freedom.

Explore correlation and association between variables using the Pearson coefficient, scatter plots, and covariance concepts, then compare linear and monotonic relationships with Spearman rank.

Explore exploratory data analysis basics using the iris dataset with matplotlib and seaborn. Define features and labels, distinguish input variables from output, and recognize a classification problem.

Import and explore the iris dataset with pandas, seaborn, and matplotlib, inspect shape and columns, and confirm a balanced 150-row dataset with three species: Setosa, Versicolor, Virginica.

Learn to create a 2d scatter plot of Iris sepal length versus sepal width with matplotlib, and avoid the default line plot by specifying scatter.

Explore two-dimensional scatter plots using matplotlib and seaborn, color-coding iris species to reveal separations between Setosa and Versicolor versus Virginica, and learn multiple plotting approaches.

Discover how three dimensional scatter plots visualize data across up to three features, improving separability and insight in multi-dimensional machine learning data.

Explore pair plots to compare all four features across every pair, revealing six unique plots and a distribution plot, with petal length and petal width best separating Setosa from others.

Learn how to visualize a feature on the x axis with a 1D scatter plot, separating Setosa, Virginica, and Versicolor by color, and relate to histogram, pdf, and cdf concepts.

Explore histograms to reveal concentration in one-dimensional data and relate them to pdf and cdf, where the area under the curve equals probability.

Explore how histograms, pdfs, and cdfs transform 1d features into distributions for iris data; learn hist plots and kernel density estimation to reveal class overlap.

Explore how histogram bins and bin width shape distributions, showing how smaller bin sizes reveal detail while smoothing yields a smoother curve, using sepal width as a practical example.

Explore histograms and pdfs, where the area under the curve equals one and the density axis indicates probability between intervals.

Learn to draw the cumulative distribution function with a code snippet, using kde to create a pdf plot and set cumulative to true for the cdf across petals and sepals.

Learn to compute mean, variance, standard deviation, and median absolute deviation with numpy snippets, using np.mean, np.std, np.median, np.percentile, and robust.mad from statsmodels.

Explore how box plots convey univariate data characteristics using the interquartile range, medians, and whiskers to identify outliers and summarize minimum and maximum values.

Explore what a violin plot is—a blend of a box plot and probability density functions—to visualize univariate data and distributions, linking histograms, pdfs, and cdfs in 2d and 3d plots.

Explore the Haberman survival dataset through exploratory data analysis with matplotlib and seaborn, inspecting 306 records and four features: age at operation, year, nodes, and survival status.

Use describe to quickly generate statistics, identify missing values, and inspect distributions; the Haberman data reveal an imbalance between survived and not survived, informing modeling approaches.

Explore univariate analysis of age, year, and nodes using histograms and distribution plots to reveal substantial overlap between survival and non-survival, with nodes under four indicating higher survival chances.

Explores bivariate analysis with age, nodes, and year using scatter and pair plots to assess survival. Highlights limits of two-dimensional visuals and the need for more complex models.

Dive into the DonorsChoose Kaggle dataset, learn hands-on data analysis with Python, and predict proposal approvals while honing data storytelling and interpretation.

Explore the Kaggle data by analyzing the train and resource CSVs. Map project IDs to connect resource needs, quantities, and prices with metadata like teacher and state.

Define data dictionary concepts and create clear data definitions, mapping project id, title, grade category, and resources, then analyze data columns to prepare for modeling and approval outcomes.

Connect Colab to Google Drive to access data analyst train.csv and resource.csv, read with pandas, inspect shapes and columns, drop missing teacher prefix rows, and note data imbalance in approvals.

Explore univariate analysis by grouping applications by state to compute approval percentages and rank states by acceptance. Also analyze prefixes and grades for their effect on approvals.

Apply univariate analysis to clean and normalize project subcategories into single terms like literacy_language, then count and sort their occurrences with a Counter to reveal literacy_language as the top category.

Explains cleaning and analyzing univariate data for project categories and subcategories, and compares approved versus not approved distributions using box plots and pdfs, noting overlap.

Perform univariate analysis on project features by engineering word counts, total price, and resource quantities, then compare approved versus not approved distributions using pdfs and separability insights.

Perform univariate analysis on the project resource summary to examine length and digit presence, revealing digits correlate with an approval rate rise from 84% to 89%, while noting method limitations.

Learn how linear algebra solves for unknowns in systems of equations, using a bank chase example to connect speeds, head start, and vector and matrix concepts.

Learn how linear algebra underpins probability, statistics, calculus, and optimization, powering data science, machine learning, and deep learning, with applications from time series to dimensionality reduction and recommender systems.

Explore the fundamentals of vectors in 1D, 2D, and 3D, including row and column forms, and distinguish scalars from vectors by magnitude and direction, with examples like temperature and speed.

Explore how a point is defined by coordinates in two, three, and higher dimensions, and apply the generalized distance formula from the Pythagoras theorem.

Understand vectors as magnitude and direction, representing points with coordinates, and learn to compute magnitude, direction, and vector operations in expanded form across dimensions.

Understand row versus column vectors, their shapes, and how vector compatibility governs multiplication and dot products. Learn how rows and columns define matrices, vectors, and the move to tensors.

Discover the transpose of a matrix, where rows become columns and shape reverses. Explore examples and note that A times its transpose yields a special kind of matrix.

Learn how to compute a vector's magnitude using the L2 norm (Euclidean distance) and convert any vector to a unit vector by dividing by its magnitude, illustrated with examples.

Learn how to perform vector addition and subtraction: ensure equal lengths and formats, add element-wise, apply dot product, and extend to n dimensions with x_i + a_i.

Explain the inverse of a vector as another vector with the same magnitude but opposite direction, so (2,3) and (-2,-3) sum to the zero vector with magnitude sqrt(13).

Explore how the dot product of vectors works and why it matters in data analysis, data science, and machine learning, with rules for compatibility and scalar results.

Multiply a vector by a scalar to scale its magnitude, keeping the direction the same. A negative scalar flips the direction, while the magnitude changes by the scalar factor.

Explore distributive properties of vectors and scalars, and learn how the angle between two vectors is defined and measured, including multiple configurations and the smallest angle.

Learn how to compute the angle between two vectors using the dot product and magnitudes, including the cos theta relationship and a perpendicular example.

Explore orthogonal vectors, which are perpendicular with a 90-degree angle and zero dot product. See examples using vectors V1 and V2 that illustrate this orthogonality.

examine orthonormal vectors, which are orthogonal and of unit magnitude. learn to convert any vector to a unit vector by dividing by its magnitude, and revisit the dot product and angle concepts.

Understand the equation of a line as a core linear algebra concept and learn to express lines using vector form and dot products, linking to linear and logistic regression.

Explore how the equation of a line is expressed in vector form w^T x plus w0, distinguishing origin and non-origin cases, and see its generalization to n dimensions.

Explore the equation of a line through the origin using w^T x = 0, showing the line is perpendicular to w and verified by a zero dot product.

Explore the line equation in vector form, where W^T x = 0 defines a line through the origin and its perpendicular W, using dot products and origin-shifted cases.

Explore projecting a vector onto a line in the plane using magnitude and angle, including projections on axes and arbitrary lines with cos theta and sine theta relationships.

Explore computing the perpendicular distance from a point to a line using the vector form W^T x + w0 = 0, dot products, and projections.

Determine the positive or negative side of a line using the signed distance w^T x / ||w|| and its extension to circles, spheres, and higher dimensions.

Define the matrix as a 2d array and compare it to vectors, explain matrix size as m by n, and illustrate row and column vectors with A11 indexing.

Master matrix operations, including element-wise addition and subtraction for the same shape, Hadamard product, and dot-product based matrix multiplication, plus converting linear equations to matrix form.

Explore transpose, symmetric, diagonal, and identity matrices; understand square matrices, symmetry across the diagonal, and how identity preserves matrices through dot products.

Explore orthonormal matrices, whose every row and column is an orthonormal vector. See how A^T A equals the identity for square matrices and why identity, diagonal, and symmetric forms arise.

Explore how to compute a matrix's inverse to perform division, and master minors, cofactors, and determinants, including 2x2 and 3x3 expansion methods.

Compute the inverse of a square matrix using determinant, cofactors, and adjoint. Discover how the inverse yields the identity and how transpose relates to the inverse in orthogonal matrices.

Explore dimensionality and why reduction aids visualization. Learn to represent data as column vectors and matrices, with rows as points and columns as features, using X and X transpose.

Explore data pre-processing with normalization and standardization to scale features, address dirty real-world data, and apply max-min normalization, ensuring consistent ranges for dimensionality reduction.

Standardize data by converting each feature to zero mean and unit variance using mu and sigma, contrasting with min-max normalization to [0,1], and applying per-column standardization for PCA.

Compute covariance and variance from data sets and matrices. Understand how to treat x and y vectors, and how column-wise means and a covariance matrix S form the covariance calculation.

Explain the covariance matrix properties, including its square and symmetric shape, and show how standardization (mu=0, standard deviation equals one) reduces covariance to X^T X divided by n-1.

Explore dimensionality reduction from a geometric standpoint, derive the PCA formula, and apply Python code to visualize data by projecting onto principal components.

Define the data matrix and mean vector, standardize to zero mean and unit variance, then project points onto a unit vector mu to maximize variance.

Explore the mathematical formulation of PCA in part 2: maximize variance via x.mu projections, with mu as a unit vector, and connect data matrix X to principal direction and variability.

Formulate PCA as a constrained optimization with the covariance matrix; solve s mu = lambda mu to obtain eigenvalues and eigenvectors, select top components, and project X onto these axes.

Explore failure cases of PCA in dimensionality reduction, including when variance across axes is similar, overlapping clusters emerge, and sinusoidal data loses information.

Explore a real data set and dimensionality in visualization, connecting Google Colab to Google Drive, access mnist train csv from Kaggle, and read it with pandas.

Understand MNIST represents handwritten digits as 28 by 28 grayscale images. These flattened 784-pixel inputs map to labels d and l across about 42k samples with 0–255 pixel values.

Visualize a single MNIST digit by reshaping a 784-pixel row into a 28 by 28 grayscale image and verify its label; then apply PCA with standardization, covariance, and eigenvectors.

Standardize the MNIST data, compute the covariance, and project onto the top two eigenvectors to visualize two-dimensional PCA; note 2D limits and the option for 3D visualization.

Learn to apply PCA with sklearn on MNIST data, standardize, compute principal components with fit_transform to reduce 42,000 samples to two components, and visualize the results.

A probability distribution function graphs the probability of each value of a random variable; discrete cases use the probability mass function.

Explore continuous random variables and probability density functions. The area under the curve between two heights gives the probability, while exact heights have zero probability.

Discover the Bernoulli distribution, a discrete two-outcome model where one outcome has probability p and the other 1-p, and its use in Bernoulli trials.

Examine the binomial distribution, an extension of the Bernoulli distribution with independent trials, probability of success p, and the binomial formula N choose K p^K (1-p)^{N-K}.

Discover how expected value, the weighted average of outcomes, guides decisions in probabilistic scenarios. A gambling example shows positive expected value predicting long-run profit via the law of large numbers.

Compute the expected value of sale changes using x times its probability, giving a long-term mean. Then derive variance and standard deviation from (x minus mean) squared times probability.

Compute the expected value for a Bernoulli distribution by multiplying outcomes 0 and 1 by their probabilities and summing, yielding E = P.

Derive the expected value of a binomial distribution from the six-ball over example with n=6 and p=0.3. Conclude that E[X] = np equals 1.8, illustrating the long-run average per over.

Explore the law of large numbers by showing how averages converge to the expected value as trials increase, illustrated with dice outcomes and counts of sixes.

Explore the normal (gaussian) distribution, a bell-shaped, continuous, symmetric curve where the area under the curve equals one, and learn how mean and standard deviation shift it to define probabilities.

Understand how standard deviation shapes the probability density function, with larger spread flattening the normal distribution and smaller spread producing a steeper peak.

Explore how histograms and cumulative distributions connect, showing how the CDF reflects the area under the PDF and how left-right areas relate in normal distributions.

Explore the normal distribution formula, its mu and standard deviation parameters, and how changing them shapes the curve, with Excel-based real-data experiments.

Explore normal distribution with a custom Excel utility to visualize how mu and sigma shape the PDF and CDF, compute them step by step, and illustrate the 68-95-99.7 rule.

Understand the standard normal distribution by transforming any normal distribution to mean zero and standard deviation one, enabling use of a z table by subtracting mu and dividing by sigma.

Explore the normal distribution and the meaning of extreme values on its left and right. Learn that the asymptotic curve assigns positive yet minuscule probabilities to distant values.

Learn how the z score standardizes any normal distribution to a unit normal, using (x−μ)/σ, and how the area under the pdf relates to probabilities between x and y.

Understand how to compute and interpret the z score as the number of standard deviations from the mean, in both original and unit normal distributions, with concrete examples.

Master how to read a z score table, interpret positive and negative z values, and use left and right area concepts under the normal distribution to solve problems.

Use the z score to assess a normal pizza size distribution with mean 16.3 in and std dev 0.2 in, finding a 6.68% chance of a free pizza.

Analyze the normal distribution with mean 16.3 and sd 0.2 by calculating z scores for pizza sizes, then find right-tail probability above 16.5 and the interval probability using the z-table.

Apply z-score calculations to a normal distribution with mean 70 and sd 5, read the z-table to estimate probabilities for x<65, x>75, and 65≤x≤75, then convert to counts.

Use z-score methods for a normal distribution to determine mu and sigma from P(X<30)=0.15 and P(X>50)=0.10 in a battery lifespan example.

Explore symmetric distributions and skewness, including mean, mode, and median relationships in normal distributions, and how positive or negative skewness shapes data.

Apply the central limit theorem to samples: the distribution of sample means becomes normal with the population mean and a standard deviation equal to population standard deviation divided by sqrt(n).

Central limit theorem states that, for any population, sampling with over 30 yields sample-means distribution centered at population mean, with standard deviation equal to population standard deviation divided by sqrt(n).

Explore central limit theorem: from any population with 30 samples, distribution of sample means is normal with mean mu and sigma over sqrt(n); if population is normal, any size suffices.

Explore how the central limit theorem and z-scores help compute the probability that a sample mean exceeds or lies between thresholds, using real-world expenditure and shopper examples.

Apply the central limit theorem to find the probability that the sample mean of 49 shoppers, with mu 448 and sigma 21, lies between 441 and 446, yielding about 24.5%.

Explore discrete and continuous uniform distributions and their relation to normal distribution. See discrete uniform's equal-probability finite outcomes, like a dice, and continuous uniform's height making area one.

Explore the log normal distribution, its link to the normal distribution via log and exponential transformations, and the implications of skew, positivity, and parameters mu and sigma.

Explore how lognormal distributions arise in everyday data, with examples from online comments, dwell time, game durations, tissue sizes, surgery times, income, citations, file sizes, and traffic.

Explore power law distributions, where one quantity changes as a power of another, producing exponential rise or fall; see income, file size, and comments as practical examples.

Explore the Pareto distribution as a power-law model with alpha, illustrating wealth, income, and other real-world patterns; learn its 80/20 intuition and diverse applications.

Explore the Pareto distribution formula, its alpha shape and beta scale parameters, and how varying these values shapes the curve and sets the minimum X for income modeling.

Explore the quantile-quantile (q-q) plot to compare an unknown distribution with a known one, especially against normal and log normal distributions, by sorting data and assessing linearity.

Use the box-cox transformation to normalize any distribution, guided by the lambda parameter; if lambda is zero, apply the log transform, and verify with visual checks and a QQ plot.

Explore how distributions guide data analysts and machine learning engineers in resource planning and analysis, using log normal and normal sizing for t shirts, Pareto storage patterns, and hypothesis testing.

Learn hypothesis testing by combining normal distribution and the central limit theorem, clarifying null and alternate hypotheses, alpha, and p value through experiments and data samples.

Construct a 90% confidence interval for a mean using a random sample, central limit theorem, and z-scores, illustrated with a US-India trade example.

Compute a 98% confidence interval for the average age of engineers using the known population standard deviation, based on a sample of 50 with mean 34.3, yielding 31.65 to 36.93.

Understand why z score and z table are limited when population standard deviation is unknown, and how the t table uses degrees of freedom and the sample standard deviation.

Test the null hypothesis that the widget average weighs 20 g using a one-tailed test with n=20; compute the t score and p value, and conclude you cannot reject null.

Explore a one-tailed hypothesis test with n=15, sample mean 11.4, std dev 2.5, testing mu=10. find t=2.168 and p=0.025, rejecting the null in favor of mean greater than ten inches.

Conduct a one-tailed t-test for mu = 82 vs mu > 82 with n = 25. 85 and s = 4.1 give t = 3.65, p ≈ 0.005, reject null.

Explore how alpha and p-values guide hypothesis testing, defining null and alternate hypotheses, and interpreting evidence levels from p values with correct rejection and not rejecting the null.