2026 Fall Math Assignments Schedule

Course Structure, Administrative Timeline, and Assessment Parameters

• Course Identification:

  • Course Code and Term: 2026 FALL(16wk) - MATH...

  • Learning Management Platform: Pearson MyLab / Mastering Pearson (mastering.pearson.com)

  • Course Format: 16-week semester structure divided into modular units, homework series, practice exams, and timed unit exams.

• Assessment Categories and Interface Indicators:

  • Homework Assignments (marked with a blue circular icon): Formative problem sets designed to establish procedural fluency and conceptual understanding.

  • Practice Exams (marked with an orange square icon): Low-stakes diagnostic reviews featuring unlimited test attempts ( \infty ), enabling iterative mastery.

  • Proctored / Formal Unit Exams (marked with a green diamond icon): Summative evaluations subject to strict time constraints (80\,\text{min}) and a fixed submission ceiling (2 attempts total).

  • Prerequisite Flagging: Certain advanced modules and exams (e.g., Unit 2 assessments) feature a green flag indicator denoting completion or grade prerequisites from prior modules.

• Master Deadlines and Submission Quotas:

  • Orientation Quiz: Due at 10:00pm.

  • Unit 1 Homework (HW 1.1 through HW 3.4): Due 12/10/26 at 10:00pm.

  • Unit 1 Practice Exam (Ch 1–3): Due 12/10/26 at 10:00pm; attempts completed: 1 \text{ of } \infty.

  • Unit 1 Exam (Ch 1–3): Due 09/21/26 at 11:59pm; duration: 80\,\text{min}; attempts completed: 1 \text{ of } 2.

  • Unit 2 Homework (HW 4.1 through HW 5.5): Due 10/09/26 at 11:59pm.

  • Unit 2 Practice Exam 2 (Ch 4–5): Due 10/09/26 at 11:59pm; attempts completed: 0 \text{ of } \infty.

  • Unit 2 Exam (Ch 4–5): Due 10/09/26 at 11:59pm; duration: 80\,\text{min}; attempts completed: 0 \text{ of } 2.

  • Midterm Practice Exam (Units 1–2): Due 10/15/26 at 11:59pm; attempts completed: 0 \text{ of } \infty.

Unit 1: Descriptive Statistics and Data Classification (Chapters 1–2)

• Chapter 1: Introduction to Statistics and Data Foundations:

  • HW 1.1 — Overview of Statistics (Due 12/10/26 at 10:00pm):

  • Core Definitions: Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data.

  • Population vs. Sample: A population encompasses the entire collection of all individuals, items, or outcomes under consideration. A sample is a representative subset of a population.

  • Parameter vs. Statistic: A parameter is a numerical measurement describing a characteristic of a population (e.g., population mean $\mu$, population standard deviation $\sigma$). A statistic is a numerical measurement describing a characteristic of a sample (e.g., sample mean $\bar{x}$, sample standard deviation $s$).

  • Branches of Statistics: Descriptive statistics involves organizing, summarizing, and displaying data via tables, charts, and calculations. Inferential statistics involves using sample data to draw conclusions, make predictions, and test hypotheses regarding a population.

  • HW 1.2 — Data Classification (Due 12/10/26 at 10:00pm):

  • Types of Data: Qualitative (categorical) data consists of attributes, labels, or non-numerical entries. Quantitative data consists of numerical measurements or counts.

  • Quantitative Subcategories: Discrete data results from finite or countable values (e.g., number of students). Continuous data results from infinitely many possible values over a continuous scale without gaps or interruptions (e.g., height, temperature, time).

  • Four Levels of Measurement:

    • Nominal: Categories only; data cannot be arranged in an ordering scheme (e.g., eye color, marital status).

    • Ordinal: Data can be arranged in order or ranked, but differences between data values are meaningless or cannot be determined (e.g., movie ratings, ranking finish in a race).

    • Interval: Ordered data where meaningful differences can be calculated; lacks an inherent (absolute) natural zero starting point (e.g., temperature in Fahrenheit or Celsius, calendar years).

    • Ratio: Ordered data with meaningful differences and a true, inherent zero point representing complete absence of the quantity; ratios between values are mathematically valid (e.g., weight, distance, income).

• Chapter 2: Descriptive Representation and Summarization:

  • HW 2.1 — Frequency Distr. & Graphs - Part 1 & Part 2 (Due 12/10/26 at 10:00pm):

  • Frequency Distribution Construction: A table that partitions data into classes (intervals) and shows the frequency $f$ of occurrences in each class.

  • Class Width Calculation Formula:

    • $\text{Class Width} = \frac{\text{Maximum Data Value} - \text{Minimum Data Value}}{\text{Number of Classes}}$

    • The calculated quotient is always rounded up to the next convenient whole number or measurement precision.

  • Class Midpoint: Calculated as the average of lower and upper class limits:

    • $\text{Midpoint} = \frac{\text{Lower Class Limit} + \text{Upper Class Limit}}{2}$

  • Relative Frequency: Proportion or percentage of data values falling within a specific class:

    • $\text{Relative Frequency} = \frac{f}{n}$

    • The sum of all relative frequencies must equal $1$ (or approximately $100\%$ allowing for rounding).

  • Cumulative Frequency: The running sum of frequencies for that class and all previous classes.

  • Graphical Displays: Frequency histograms, relative frequency histograms, frequency polygons (midpoints plotted against frequencies), and ogives (cumulative frequency plotted against upper class boundaries).

  • HW 2.2 — More Graphs & Displays - Part 1 & Part 2 (Due 12/10/26 at 10:00pm):

  • Stem-and-Leaf Displays: Preserves original data values while displaying data shape; consists of a stem (leading digits) and a leaf (trailing digit), accompanied by an explanatory key.

  • Dot Plots: Displays discrete numerical data by placing dots above a horizontal axis corresponding to each data observation.

  • Pie Charts: Circular statistical graphic divided into proportional slices representing categorical data relative frequency, where slice angle is $\text{Degrees} = \frac{f}{n} \times 360^{\circ}$.

  • Pareto Charts: Bar graph for qualitative data where bars are sorted in descending order of frequency or relative frequency, paired with an optional cumulative line.

  • Paired Data Displays: Scatter plots for bivariate data pairs $(x, y)$ to observe correlation patterns; time-series plots depicting quantitative variables across sequential temporal increments.

  • HW 2.3 — Measures of Central Tendency - Part 1 & Part 2 (Due 12/10/26 at 10:00pm):

  • Sample Mean:

    • $\bar{x} = \frac{\sum x}{n}$

  • Population Mean:

    • $\mu = \frac{\sum x}{N}$

  • Median: The physical center value of an ordered dataset. For sample size $n$, if $n$ is odd, the median is the middle value; if $n$ is even, the median is the arithmetic mean of the two middle values.

  • Mode: The data value that occurs with the greatest frequency. Datasets can be unimodal, bimodal, multimodal, or have no mode.

  • Weighted Mean: Accounting for varying weights assigned to individual observations:

    • $\bar{x}_w = \frac{\sum (w \cdot x)}{\sum w}$

  • Mean of Grouped Frequency Distribution:

    • $\bar{x} = \frac{\sum (f \cdot x_m)}{n}$

    • Where $x_m$ is the midpoint of each class and $n = \sum f$.

  • Distribution Shapes: Symmetric (mean, median, and mode coincide), skewed right/positively skewed (mean pulled right, $\text{Mean} > \text{Median}$), and skewed left/negatively skewed (mean pulled left, $\text{Mean} < \text{Median}$).

• Chapter 2: Variation and Positional Measures:

  • HW 2.4 — Measures of Variation - Part 1 & Part 2 (Due 12/10/26 at 10:00pm):

  • Range: Difference between the highest and lowest data values:

    • $\text{Range} = \text{Maximum Value} - \text{Minimum Value}$

  • Population Variance and Standard Deviation:

    • $\sigma^2 = \frac{\sum (x - \mu)^2}{N}$

    • $\sigma = \sqrt{\frac{\sum (x - \mu)^2}{N}}$

  • Sample Variance and Sample Standard Deviation (Bessel's Correction):

    • $s^2 = \frac{\sum (x - \bar{x})^2}{n - 1}$

    • $s = \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}}$

  • Empirical Rule (68–95–99.7 Rule for Bell-Shaped/Symmetric Distributions):

    • Approximately $68\%$ of all data values fall within $1$ standard deviation of the mean: $[\mu - \sigma, \mu + \sigma]$.

    • Approximately $95\%$ of all data values fall within $2$ standard deviations of the mean: $[\mu - 2\sigma, \mu + 2\sigma]$.

    • Approximately $99.7\%$ of all data values fall within $3$ standard deviations of the mean: $[\mu - 3\sigma, \mu + 3\sigma]$.

  • Chebychev's Theorem (Applies to Any Distribution Shape):

    • For any dataset and any real number $k > 1$, the minimum proportion of data lying within $k$ standard deviations of the mean is:

    • $\text{Proportion} \ge 1 - \frac{1}{k^2}$

    • For $k = 2$, at least $1 - \frac{1}{4} = 75\%$ of data falls in $[\mu - 2\sigma, \mu + 2\sigma]$.

    • For $k = 3$, at least $1 - \frac{1}{9} = 88.89\%$ of data falls in $[\mu - 3\sigma, \mu + 3\sigma]$.

  • HW 2.5 — Measures of Position - Part 1 & Part 2 (Due 12/10/26 at 10:00pm):

  • Standardized Score (z-Score): Measures the number of standard deviations a data value $x$ lies above or below the mean:

    • $z = \frac{x - \mu}{\sigma}$

    • $z = \frac{x - \bar{x}}{s}$

    • A value is generally considered unusual if $|z| > 2$, and very unusual/outlier if $|z| > 3$.

  • Quartiles and Interquartile Range (IQR):

    • First Quartile $Q_1$: 25th percentile.

    • Second Quartile $Q_2$: 50th percentile (the median).

    • Third Quartile $Q_3$: 75th percentile.

    • $IQR = Q_3 - Q_1$

  • Outlier Identification Boundaries (Fences):

    • $\text{Lower Fence} = Q_1 - 1.5 \cdot IQR$

    • $\text{Upper Fence} = Q_3 + 1.5 \cdot IQR$

  • Five-Number Summary: Includes the $\text{Minimum}$, $Q_1$, $\text{Median} (Q_2)$, $Q_3$, and $\text{Maximum}$.

  • Box-and-Whisker Plot: Graphical representation constructed using the five-number summary and indicating potential outliers via whiskers extended to non-outlier limits.

Unit 1: Probability and Counting Foundations (Chapter 3)

• Chapter 3: Fundamentals of Probability and Counting Techniques:

  • HW 3.1 — Basic Concepts (Probability & Counting) - Part 1 & Part 2 (Due 12/10/26 at 10:00pm):

  • Sample Space and Events: Sample space $S$ is the set of all possible outcomes. An event $E$ is a subset of $S$.

  • Probability Axioms:

    • For any event $E$, $0 \le P(E) \le 1$.

    • For the entire sample space, $P(S) = 1$.

  • Three Approaches to Probability:

    • Classical (Theoretical) Probability: Assumes equally likely outcomes:

    • $P(E) = \frac{n(E)}{n(S)}$

    • Empirical (Statistical) Probability: Based on direct observations or trials:

    • $P(E) = \frac{\text{Frequency of Event } E}{\text{Total Number of Observations}}$

    • Subjective Probability: Based on intuition, experience, or educated estimation.

  • Law of Large Numbers: As an experiment is repeated many times, the empirical probability of an event approaches its theoretical probability.

  • Complement of an Event: The event that $E$ does not occur, denoted $E'$ or $E^c$:

    • $P(E') = 1 - P(E)$

  • Fundamental Counting Principle: If event 1 can occur in $m$ ways and event 2 can occur in $n$ ways, the sequence can occur in $m \cdot n$ ways. Extended to $k$ sequential selections:

    • $\text{Total Outcomes} = n_1 \cdot n_2 \cdot n_3 \cdots n_k$

  • HW 3.2 — Cond. Probability & Mult. Rule - Part 1 & Part 2 (Due 12/10/26 at 10:00pm):

  • Conditional Probability: Probability of event $B$ occurring given that event $A$ has already occurred:

    • $P(B|A) = \frac{P(A \cap B)}{P(A)}$

    • Provided $P(A) > 0$.

  • Multiplication Rule for Compound Events:

    • $P(A \cap B) = P(A) \cdot P(B|A)$

  • Independent vs. Dependent Events: Two events $A$ and $B$ are independent if the occurrence of one does not affect the probability of the other, meaning $P(B|A) = P(B)$ or $P(A|B) = P(A)$.

  • Multiplication Rule for Independent Events:

    • $P(A \cap B) = P(A) \cdot P(B)$

  • HW 3.3 — Addition Rule (Due 12/10/26 at 10:00pm):

  • General Addition Rule: For any two events $A$ and $B$:

    • $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

  • Mutually Exclusive (Disjoint) Events: Events that cannot occur simultaneously, meaning $P(A \cap B) = 0$.

  • Addition Rule for Mutually Exclusive Events:

    • $P(A \cup B) = P(A) + P(B)$

  • HW 3.4 — Probability & Counting (Addtl. Topics) - Part 1 & Part 2 (Due 12/10/26 at 10:00pm):

  • Factorial Notation: For any non-negative integer $n$, $n! = n \cdot (n - 1) \cdot (n - 2) \cdots 1$, with the definition $0! = 1$.

  • Permutations of $n$ Distinct Items Taken $r$ at a Time (Order Matters):

    • $_n P_r = \frac{n!}{(n - r)!}$

  • Distinguishable Permutations of Repeated Items:

    • For $n$ objects where $n_1$ are of type 1, $n_2$ of type 2, up to $n_k$ of type $k$:

    • $\text{Permutations} = \frac{n!}{n_1! \cdot n_2! \cdots n_k!}$

  • Combinations of $n$ Distinct Items Taken $r$ at a Time (Order Does Not Matter):

    • $_n C_r = \binom{n}{r} = \frac{n!}{r! \cdot (n - r)!}$

• Unit 1 Assessment Specifications:

  • Unit 1 Practice Exam (Ch 1–3):

  • Due Date and Time: 12/10/26 at 10:00pm.

  • Attempt Structure: Unlimited attempts permitted (1 \text{ of } \infty completed).

  • Function: Comprehensive diagnostic benchmark covering data collection, descriptive tables/graphs, variation, position, and counting/probability.

  • Unit 1 Exam (Ch 1–3):

  • Due Date and Time: 09/21/26 at 11:59pm.

  • Testing Duration: 80\,\text{min}.

  • Attempt Quota: 2 total attempts allowed (1 \text{ of } 2 completed).

  • Scope: Formal summative assessment testing foundational statistics through probability rules.

Unit 2: Discrete Probability Distributions (Chapter 4)

• Chapter 4: Discrete Random Variables and Associated Models:

  • HW 4.1 — Probability Distributions - Part 1 & Part 2 (Due 10/09/26 at 11:59pm):

  • Random Variable: A variable $x$ whose numerical values are determined by the outcome of a probability experiment.

  • Discrete Probability Distribution Requirements:

    • $\sum P(x) = 1$

    • $0 \le P(x) \le 1$

  • Mean (Expected Value) of a Discrete Random Variable:

    • $\mu = E(x) = \sum [x \cdot P(x)]$

  • Variance and Standard Deviation of a Discrete Probability Distribution:

    • $\sigma^2 = \sum [(x - \mu)^2 \cdot P(x)] = \left( \sum [x^2 \cdot P(x)] \right) - \mu^2$

    • $\sigma = \sqrt{\sigma^2}$

  • HW 4.2 — Binomial Distributions (Due 10/09/26 at 11:59pm):

  • Criteria for a Binomial Experiment:

    • Fixed number of independent trials $n$.

    • Only two mutually exclusive outcomes per trial: success $S$ or failure $F$.

    • Constant probability of success on each trial: $P(S) = p$, and probability of failure: $P(F) = q = 1 - p$.

    • The random variable $x$ counts the total number of successes: $x \in \{0, 1, 2, \dots, n\}$.

  • Binomial Probability Formula:

    • $P(x) = \binom{n}{x} p^x q^{n - x} = \frac{n!}{x! \cdot (n - x)!} p^x q^{n - x}$

  • Statistical Parameters of a Binomial Distribution:

    • Mean:

    • $\mu = n \cdot p$

    • Variance:

    • $\sigma^2 = n \cdot p \cdot q$

    • Standard Deviation:

    • $\sigma = \sqrt{n \cdot p \cdot q}$

  • HW 4.3 — More Discrete Probability Distributions (Due 10/09/26 at 11:59pm):

  • Geometric Distribution: Models the number of trials $x$ until the first success occurs in repeated independent trials with constant success probability $p$:

    • $P(x) = q^{x - 1} \cdot p$

    • Mean and Variance:

    • $\mu = \frac{1}{p}$

    • $\sigma^2 = \frac{q}{p^2}$

  • Poisson Distribution: Models the number of occurrences $x$ of an event over a specified interval of time, space, or volume, with mean occurrence rate $\mu$:

    • $P(x) = \frac{\mu^x \cdot e^{-\mu}}{x!}$

    • Standard Deviation:

    • $\sigma = \sqrt{\mu}$

Unit 2: Continuous and Normal Probability Distributions (Chapter 5)

• Chapter 5: Normal Distribution Modeling and Inference Principles:

  • HW 5.1 — Normal & Standard Normal Distributions (Due 10/09/26 at 11:59pm):

  • Properties of Normal Distributions: Continuous, bell-shaped, symmetric about the mean $\mu$; total area under the probability density curve equals $1$; asymptotic to the horizontal axis; inflection points occur at $\mu \pm \sigma$.

  • Standard Normal Distribution: Defined as a continuous normal distribution with mean $\mu = 0$ and standard deviation $\sigma = 1$, denoted $Z \sim N(0, 1)$.

  • Cumulative Standard Normal Distribution:

    • $P(Z \le z) = \int_{-\infty}^z \frac{1}{\sqrt{2\pi}} e^{-\frac{u^2}{2}}\,du$

  • HW 5.2 — Normal Distributions (Finding Probabilities) (Due 10/09/26 at 11:59pm):

  • Standardization Process: Transforming an arbitrary non-standard normal variable $X \sim N(\mu, \sigma^2)$ into standard units:

    • $z = \frac{x - \mu}{\sigma}$

  • Probability Calculation Strategies:

    • Probability to the left of $x$: $P(X < x) = P\left(Z < \frac{x - \mu}{\sigma}\right)$.

    • Probability to the right of $x$: $P(X > x) = 1 - P\left(Z < \frac{x - \mu}{\sigma}\right)$.

    • Probability between $x_1$ and $x_2$: $P(x_1 < X < x_2) = P(Z < z_2) - P(Z < z_1)$.

  • HW 5.3 — Normal Distributions (Finding Values) (Due 10/09/26 at 11:59pm):

  • Inverse Normal Transformation: Solving for a specific raw score $x$ corresponding to a given percentile or cumulative tail area $P$:

    • Find the critical standard normal value $z$ such that $P(Z \le z) = \text{Area}$.

    • Transform $z$ back to raw score units:

    • $x = \mu + z \cdot \sigma$

  • HW 5.4 — Sampling Distr. & Central Limit Thm. (Due 10/09/26 at 11:59pm):

  • Sampling Distribution of the Sample Mean: Distribution of means $\bar{x}$ obtained from all possible random samples of size $n$ drawn from a population.

  • Properties of the Sampling Distribution:

    • Mean of the sample means:

    • $\mu_{\bar{x}} = \mu$

    • Standard Error of the Mean (standard deviation of sample means):

    • $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$

  • Central Limit Theorem (CLT):

    • If a population has mean $\mu$ and standard deviation $\sigma$, then as sample size $n$ increases, the sampling distribution of $\bar{x}$ approaches a normal distribution regardless of the underlying population shape.

    • Operational Threshold: When $n \ge 30$, the sampling distribution is approximately normal. If the original population is already normal, the sampling distribution of $\bar{x}$ is normally distributed for any sample size $n$.

  • Standardized Score for Sample Mean:

    • $z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

  • HW 5.5 — Normal Approx. to Binomial Distr. (Due 10/09/26 at 11:59pm):

  • Justification and Criteria for Normal Approximation: A binomial random variable with parameters $n$ and $p$ can be approximated by a normal distribution with $\mu = n \cdot p$ and $\sigma = \sqrt{n \cdot p \cdot q}$ provided:

    • $n \cdot p \ge 5$

    • $n \cdot q \ge 5$

  • Continuity Correction Factor: Correcting for the transition from a discrete integer count to a continuous area by expanding the discrete integer value by $\pm 0.5$:

    • For $P(X = x)$, evaluate $P(x - 0.5 < X < x + 0.5)$.

    • For $P(X \ge x)$, evaluate $P(X > x - 0.5)$.

    • For $P(X > x)$, evaluate $P(X > x + 0.5)$.

    • For $P(X \le x)$, evaluate $P(X < x + 0.5)$.

    • For $P(X < x)$, evaluate $P(X < x - 0.5)$.

• Unit 2 Assessment Specifications:

  • Unit 2 Practice Exam 2 (Ch 4–5):

  • Status and Indicators: Accompanied by a green prerequisite flag.

  • Due Date and Time: 10/09/26 at 11:59pm.

  • Attempt Structure: Unlimited attempts permitted (0 \text{ of } \infty completed).

  • Function: Comprehensive preparation covering discrete probability variables, binomial distributions, normal distributions, the Central Limit Theorem, and normal approximations.

  • Unit 2 Exam (Ch 4–5):

  • Status and Indicators: Accompanied by a green prerequisite flag.

  • Due Date and Time: 10/09/26 at 11:59pm.

  • Testing Duration: 80\,\text{min}.

  • Attempt Quota: 2 total attempts allowed (0 \text{ of } 2 completed).

  • Scope: Formal summative exam on Chapters 4 and 5.

Comprehensive Midterm Review and Integrated Curriculum

• Midterm Practice Exam (Units 1–2):

  • Due Date and Time: 10/15/26 at 11:59pm.

  • Attempt Quota: Unlimited attempts permitted (0 \text{ of } \infty completed).

  • Scope: Comprehensive evaluation synthesizing the full curricular scope across Unit 1 and Unit 2 (Chapters 1 through 5).

• Core Knowledge Checkpoints Across Chapters 1–5:

  • Chapter 1: Data classification, levels of measurement, parameter vs. statistic, sample vs. population.

  • Chapter 2: Frequency distributions, histogram generation, central tendency (mean, median, mode), variation (variance, standard deviation, empirical rule, Chebychev's theorem), and position (quartiles, boxplots, z-scores).

  • Chapter 3: Probability foundations, compound events, addition rule for disjoint events, conditional probability, multiplication rule for independent/dependent events, permutations, and combinations.

  • Chapter 4: Discrete probability distributions, expectation $E(x) = \mu$, variance, and binomial distribution formulas.

  • Chapter 5: Continuous standard normal curves, z-score transformations, inverse normal calculations, Central Limit Theorem standard error $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$, and continuity corrections for normal approximation.