MATH 158: Introductory Data Analysis Syllabus – Key Topics and Structure

Course Overview

This syllabus outlines the structure, main topics, and grading policy for MATH 158: Introductory Data Analysis. The course covers foundational concepts in statistics, including data types, descriptive statistics, probability, hypothesis testing, and probability distributions. The course is designed to provide students with practical and theoretical knowledge essential for analyzing and interpreting data.

Course Topics and Weekly Structure

Week	Main Topics
1	Introduction, using Canvas and Pearson MyLab, IR1: Data Definitions, Types, Sets, Sections
2	IR2: Data Types, Scales, Summaries
3	Sample Completion of Ch 1 Assignment
4	2.4: Graphs & Summaries
5	2.5: Graphs & Summaries
6	2.6: Measures of Center
7	2.7: Measures of Variation
8	2.8: Standard Deviation, Empirical Rule
9	3.4: Range Rule of Thumb, Confidence Intervals
10	4.1: Probability, Random Variables
11	4.2: Probability Rules, Conditional Probability
12	4.3: Probability Applications, Simulations
13	5.1: Binomial Distribution, Probability, Range Rule, Tails, Confidence Intervals
14	5.2: Binomial Distribution with Mean & Std Dev, Inequality Complements
15	Final Exam

Key Topics Explained

Introduction to Data Analysis

• Data Types: Understanding qualitative vs. quantitative data, scales of measurement (nominal, ordinal, interval, ratio).

• Data Summaries: Organizing and summarizing data using tables and graphs.

Descriptive Statistics

• Measures of Center: Mean, median, and mode are used to describe the central tendency of a dataset.

• Measures of Variation: Range, variance, and standard deviation quantify the spread of data.

• Empirical Rule: For normal distributions, approximately 68%, 95%, and 99.7% of data fall within 1, 2, and 3 standard deviations from the mean, respectively.

Probability

• Probability Rules: Basic rules include the addition and multiplication rules, as well as the concept of conditional probability.

• Random Variables: Variables whose values are determined by the outcome of a random phenomenon.

Probability Distributions

• Binomial Distribution: Describes the number of successes in a fixed number of independent Bernoulli trials.

• Mean and Standard Deviation of Binomial Distribution: $\mu = np$ $\sigma = \sqrt{npq}$ where $n$ is the number of trials, $p$ is the probability of success, and $q = 1 - p$.

Inferential Statistics

• Confidence Intervals: Range of values used to estimate a population parameter with a certain level of confidence.

• Hypothesis Testing: Procedure for testing claims about a population using sample data.

Grading Policy

• Final Weighted Average: Calculated by dividing the total points earned by the total possible points. Letter grades are assigned based on percentage cutoffs (A: ≥ 92%, B: 82–91%, C: 72–81%, D: 62–71%, F: < 62%).

• Attendance: Missing assignments or more than 2 weeks of attendance may result in a lower grade.

Additional Information

• Course materials are accessed via Pearson MyLab and Canvas.

• Assignments, discussions, and exams are scheduled weekly.

• Students are encouraged to use the Integrated Review Guide Workbook for exercises and practice.