Vis Analytics

Administrative and Exam Logistics

• There are extra copies of some material at the bookstore; if you didn’t order one, they’ll be available at the bookstore when they arrive.

• A video on Excel charts and graphs was planned for upload over the weekend; it will be posted eventually, not required immediately.

• Personal update: the instructor’s mother went to the hospital Friday night and passed away Sunday; weekend work was affected.

• Class impact: services will be next week by next Friday, but this will not affect the class schedule; class will meet Tuesday and Thursday as usual.

• If a student feels they didn’t receive a response or need something, please reach out again; the instructor will respond; the goal is ensure students have what they need, especially with an upcoming test.

• Exam logistics:

  • The exam is worth 75 points total, with 38 questions at 2 points each, totaling 76 possible points.

  • The class aims for 900 out of 1000 points overall; this exam contributes to that total.

  • The exam will be completed in class on student computers; if you normally use an iPad, bring a laptop; if you don’t have a laptop, notify the instructor and they’ll help arrange one (library options available).

  • For students in the back row, there will be a temporary relocation to the back row during the exam, and the exam duration is approximately one hour.

  • The in-class exam environment is designed so most students can complete it without a lockdown browser; the exam uses an in-platform system with shuffled questions and algorithmic numbers to minimize cheating.

  • Excel will be used similarly to the homework; you should be comfortable with Excel tasks, as homework will be reflected on the test.

• Exam preparation guidance:

  • Review all homework in MyLab (not the reading or try-it portions, but the actual homework assignments—one per chapter).

  • The test will reflect the same look and feel as homework; most questions come from previous homework, with some from the Week 1 quiz (history of data visualization).

  • Learn the vocabulary from chapters 1–4; the textbook contains blue-highlighted boxes with definitions; there is no prebuilt flashcard set in the publisher’s system, so students should create their own flashcards or use index cards.

  • Access the Gradebook and use the Review feature to revisit what you did on homework and read the questions.

• General study approach:

  • Chapters 1–4 vocabulary and core concepts should be reviewed thoroughly; focus on definitions and how terms are used in context.

  • The instructor recommends active study strategies (e.g., index cards, reviewing blue boxes, and summarizing key ideas).

Core Concepts in this Unit

• Two main branches of statistics:

  • Descriptive statistics (descriptive analytics, exploratory data analysis): describe data, summarize features, and tell clear stories about datasets.

  • Inferential statistics: take information from a sample to make inferences about a population.

• Descriptive analytics focus: exam-like measures (mean, median, mode, variability, shape, and associations) used to describe current/historical data and set benchmarks; forecasting involves using past data to project future outcomes.

• Data storytelling and real-world context:

  • Stories in each chapter illustrate how descriptive statistics and analytics are used in business contexts.

  • Sam’s vignette (buying a used car) introduces concepts like central tendency, variability, shape, and outliers in a practical setting.

• Foundational terms:

  • Central tendency: measures that describe the center of a dataset (mean, median, mode).

  • Variability (spread): how far data points are from each other (range, variance, standard deviation).

  • Shape of distribution: skewness and symmetry (left-skewed, right-skewed, symmetrical).

  • Associations: relationships between two quantitative variables (as seen in scatter plots).

  • Descriptive analytics (EDA): using statistics to describe and summarize data features, often with visualizations.

• Real-world examples and contexts:

  • A large dataset example for car data (426,000 entries) illustrating the practical challenges of working with big data and how to summarize it.

  • Shopify case study shows Pareto-based insights (80/20) driving business decisions.

Descriptive Statistics and Descriptive Analytics

• Descriptive statistics are basic data descriptions that typically fall into four categories:

  • Central tendency (mean, median, mode)

  • Variability (range, variance, standard deviation)

  • Shape of distribution (skewness, symmetry, outliers)

  • Associations (relationships between variables in a dataset)

• Descriptive analytics (EDA) expands on these ideas by using statistical techniques to describe and summarize data features, often with visual metrics.

• Forecasting context: describe past data to infer possible future trends; example from business: forecasting notebook sales by analyzing past 12–18 months of sales data.

• Chapter vignette context: Sam buys a car using a dataset and concepts from descriptive statistics to understand the market and expected values.

• Data and case studies in the chapter:

  • Used-car dataset (example): fields included ID, price, year, model, condition, cylinders, fuel, odometer, transmission, vehicle type, state, etc.; illustrates handling large data and the need for descriptive summaries before deeper analyses.

  • Shopify example (case study): categorizes product lines by revenue share (e.g., products A, B, C contributing 80%, 15%, 5% of revenue) and emphasizes the Pareto principle in practice.

• Pareto principle (80/20 rule): a recurring theme in business analytics:

  • 80% of results often come from 20% of causes.

  • The rule helps focus attention on the “vital few” causes, products, or customers that generate the majority of outcomes, with the remaining 80% having diminished returns.

  • Applications and caveats:

  • Product focus: 80% of revenue from 20% of products; 20% of products may occupy most warehouse space; decisions on inventory and product focus should consider this.

  • Customer focus: 20% of customers may generate 80% of revenue; consider targeting and servicing these key customers more intensively, while maintaining service for the rest.

  • HR and operational considerations: 80% of HR problems may originate from 20% of employees; similarly for customer complaints.

  • Important caveat: the exact percentages can vary (e.g., 75/25, 82/18); the principle is about prioritizing the vital few rather than ignoring the rest.

• Practical implications for study and business analyses:

  • Pareto analyses help streamline decision-making, inventory management, and resource allocation.

  • The approach helps identify where to invest energy and which areas to trim to avoid waste.

Central Tendency

• Definition: central tendency describes the value around which data clusters; it represents the middle or typical value of a dataset.

• The main measures:

  • Mean (average):

  • Formula: ar{x} = rac{1}{n}
    abla
    abla
    abla{i=1}^n xi (i.e., the sum of all observations divided by the number of observations)

  • Median: the middle value of a sorted dataset; if even n, the average of the two middle values.

  • Mode: the most frequently occurring value(s) in the dataset; can be unimodal or multimodal.

• Trimmed means:

  • 90% trimmed mean concept (as discussed in class): remove the extreme values from the ends to focus on the central 90% of the data; for a small example, this was described as removing 5 values from each end when there are 12 data points (
    note: this example in the lecture appeared to mix the 90% trim with a 10% edge case; the standard interpretation is to trim 5% from each end when you have a reasonably large dataset, leaving the central 90%).

• Example context (used car dataset and average price):

  • Reported mean price: ar{x} = 26.05 ext{ (thousands)}

  • Reported 90% trimmed mean: ext{trimmed mean} ext{ (central 90%)} o 21.04 ext{ (thousands)}

  • Median price: $ext{median} = 20{,}000 ext{ (assuming dollars and thousands context)}$

• Interpreting mean vs median and distribution shape:

  • If the mean and median are equal or very close, the distribution is roughly symmetric.

  • If the mean is greater than the median, the distribution is skewed to the right (positive skew).

  • If the mean is less than the median, the distribution is skewed to the left (negative skew).

• Example intuition:

  • In the car example, a higher mean price relative to the median suggests some high-priced outliers pulling the average up, resulting in right skew.

Variability and Shape of the Distribution

• Variability (spread) describes how dispersed data are around the center.

• Common measures:

  • Range: $R = ext{max}(x<em>i) - ext{min}(x</em>i)$

  • Variance:

  • For a population: \sigma^2 = rac{
    abla{i=1}^n (xi - ar{ ext{ }x})^2}{n}

  • For a sample: s^2 = rac{
    abla{i=1}^n (xi - ar{x})^2}{n-1}

  • Standard deviation:

  • Population: \sigma =
    abla \surd
    abla^2 = \surd igl( rac{
    abla{i=1}^n (xi - ar{x})^2}{n}igr)

  • Sample: s = \surd s^2 = \surd igl( rac{
    abla{i=1}^n (xi - ar{x})^2}{n-1}igr)

• Key interpretation:

  • Smaller standard deviation indicates data are less variable around the mean; greater standard deviation indicates more spread and variability.

• Worked example context (odometer readings):

  • Range example: from 0 to 218{,}000 miles, range ≈ 218{,}000 miles (illustrative reading from the dialogue).

  • Variance example from the walkthrough: a set of squared deviations summed to 484; with n = 12, the variance (sample) is $s^2 = \frac{484}{11} = 44.$

  • Standard deviation: $s = \sqrt{44} \approx 6.63.$ (units corresponding to the data, e.g., thousands of miles if data were in thousands.)

• Relationship among mean, median, and mode for distribution shape:

  • When the data are roughly symmetrical, mean = median = mode.

  • If the distribution is skewed, mean ≠ median; the direction of skewness affects which statistic is pulled toward the tail.

• The empirical rule (for approximately normal distributions):

  • About 68% of data within 1 standard deviation: P(|X - ar{x}| \,\le\, s) \approx 0.68

  • About 95% within 2 standard deviations: P(|X - ar{x}| \,\le\, 2s) \approx 0.95

  • About 99.7% within 3 standard deviations: P(|X - ar{x}| \,\le\, 3s) \approx 0.997

• Z-scores:

  • Definition: $z = \frac{x - \bar{x}}{s}$ (how many standard deviations an observation is from the mean).

  • Z-scores help compare data points across different scales.

Practical Calculations: Hand and Excel Approaches

• Hand calculations (illustrative steps used in the lecture):

  • Step 1: Arrange data in ascending order to reduce mistakes and make it easy to locate the min, max, range, and median.

  • Step 2: Compute the mean: $\bar{x} = \frac{1}{n} \sum<em>{i=1}^n x</em>i$. In the example, the sum was 228 with n = 12, giving $\bar{x} = \frac{228}{12} = 19.$ (units consistent with the data, e.g., thousands of dollars)

  • Step 3: Compute the median for n = 12 (even): the middle two values are the 6th and 7th values; the median is the average of these two. In the example, the median turned out to be 19 (same as the mean in this case).

  • Step 4: Determine the mode(s): the value(s) that occur most frequently; in the example, the modes were 15 and 22 (bimodal).

  • Step 5: Compute the range: $R = \max(x<em>i) - \min(x</em>i);$ in the example, range = 30 - 10 = 20.

  • Step 6: Compute the variance (sample, per the lecture):

  • Compute each deviation: $x<em>i - \bar{x}$, square them, sum: (\sum (xi - \bar{x})^2 = 484).

  • Then divide by (n - 1): $s^2 = \frac{484}{11} = 44.$

  • Step 7: Compute the standard deviation: $s = \sqrt{44} \approx 6.63.$

  • Step 8: Interpret the spread around the mean using the standard deviation and, if helpful, the 68-95-99.7 rule.

• Excel implementation (as demonstrated):

  • Mean: $\bar{x} = \text{=AVERAGE(range)}$

  • Median: $\text{=MEDIAN(range)}$

  • Mode (all modes): $\text{=MODE.MULT(range)}$ (Excel will spill multiple values; ensure you have space to display all modes)

  • Range: $\text{=MAX(range)} - \text{=MIN(range)}$

  • Variance (sample): $\text{=VAR.S(range)}$

  • Standard deviation (sample): $\text{=STDEV.S(range)}$

• Notes on Excel nuances (as discussed):

  • Excel has multiple variants of mode (MODE.SNGL vs MODE.MULT); use MODE.MULT to capture multiple modes.

  • When using MODE.MULT, Excel may spill results into adjacent cells; plan the layout accordingly.

  • If you see an “overflow” or spill issue with the Mode function, ensure the destination range has enough empty cells for all mode values.

Exam Guidance and Preparation Tips

• Exam format and expectations:

  • 75 points total; 38 questions at 2 points each (total = 76, but the official total is stated as 75 points in the session); the discrepancy is likely due to specific scoring rules or a rounding convention; treat the 75-point total as the stated exam score.

  • Most questions will resemble homework problems; some questions will include content from the Week 1 quiz (history of data visualization).

  • The exam will be taken in-class on a computer; bring a laptop if you don’t typically use one (library laptops available if needed).

  • No notes allowed; one attempt; no lockdown browser required for this exam; questions will be randomized with algorithmic components to prevent cheating; Excel may be used for data-entry/computations, as with homework.

• Study resources and strategy:

  • Focus your review on homework assignments in MyLab (one per chapter) as the primary source for exam content.

  • Review vocabulary terms across chapters 1–4; use blue-highlighted boxes in the textbook for quick reference to definitions.

  • Use the Gradebook review feature to reread questions and understand the expected solutions.

  • Practice flashcards or index cards for vocabulary since the textbook’s built-in flashcards are not pre-populated in this course platform.

• Key content areas to master for the unit:

  • Descriptive statistics and descriptive analytics concepts (central tendency, variability, shape, associations).

  • Distinctions between descriptive vs. inferential statistics; why inferences are drawn from samples to populations.

  • Central tendency measures (mean, median, mode) and the construction/use of a trimmed mean (e.g., 90% trimmed mean) and its purpose (outlier resistance).

  • Variability measures (range, variance, standard deviation) and their interpretation in real data contexts.

  • Shape and distribution concepts (skewness, symmetry) and their impact on mean/median interpretations.

  • Z-scores and the empirical rule for normal distributions (68-95-99.7).

  • Practical interpretation of the Pareto principle (80/20) and its business implications (revenue concentration, inventory decisions, customer focus, and HR considerations).

• Real-world connections and examples to reinforce concepts:

  • Shopify case study demonstrates how a platform’s analytics might show that 80% of revenue comes from 20% of products; helps prioritize product development and marketing efforts.

  • Pareto principle applied to customers, products, inventory, and HR problems; illustrates how distributional insights influence resource allocation and strategic decisions.

  • The instructor highlights a use-case for a large dataset (426,000 observations) to illustrate the practical challenges of descriptive analytics in big data contexts.

Quick Reference: Formulas and Key Values (LaTeX)

• Mean (sample or population is the same for the formula, but denoms differ in variance):

  • $\bar{x} = \frac{1}{n} \sum<em>{i=1}^n x</em>i$

• Median: value at the middle of an ordered list (average of the two middle values if n is even).

• Mode: most frequent value(s) in the data.

• Range:

  • $R = \max<em>i x</em>i - \min<em>i x</em>i$

• Variance and Standard Deviation:

  • Population variance: $\sigma^2 = \frac{1}{n}\sum<em>{i=1}^n (x</em>i - \mu)^2$

  • Sample variance: $s^2 = \frac{1}{n-1}\sum<em>{i=1}^n (x</em>i - \bar{x})^2$

  • Population standard deviation: $\sigma = \sqrt{\sigma^2}$

  • Sample standard deviation: $s = \sqrt{s^2}$

• Z-score:

  • $z = \frac{x - \bar{x}}{s}$

• Empirical rule (approximate for normal distributions):

  • Within 1 standard deviation: ~68%

  • Within 2 standard deviations: ~95%

  • Within 3 standard deviations: ~99.7%

• Trimmed mean (conceptual): remove a fixed percentage of the extreme values from both ends and compute the mean on the remaining data (e.g., central 90% of data).

Final Takeaways

• Descriptive statistics and descriptive analytics provide the foundational tools for summarizing data and telling stories with numbers.

• The Pareto principle is a powerful heuristic for prioritization in business analytics and decision-making.

• When interpreting data, compare mean and median to infer distribution shape and consider outliers via trimmed means or standard deviation.

• Excel is a practical tool for doing these calculations, but understanding the underlying formulas is essential for proper interpretation and flexibility in analysis.

• For exams, expect a blend of hand-calculation practice and Excel-based problems; focus on one-per-chapter homework as the primary guide to future questions.