Athabasca University MATH 215 Introduction to Statistics course outline and lessons

The course map includes Descriptive Statistics, Probability, Probability Distributions, and 3 other sections. Follow the complete section list above for the full study path.

درس مقدمه‌ای بر آمار (MATH 215) چه مباحثی دارد؟ از جمله مباحث این درس آمار توصیفی، احتمال، توزیع‌های احتمال است. فهرست کامل بخش‌ها در بالای صفحه قرار دارد.

16 of 44 written lessons are currently published and free to read. Open a linked lesson in the section map above. Check the official course outline for exact requirements.

درس‌ها و سرفصل رسمی مقدمه‌ای بر آمار (MATH 215) را از کجا پیدا کنم؟ اکنون 16 درس از 44 درس نوشتاری منتشر شده و خواندن آن‌ها رایگان است. درس‌های دارای پیوند را در نقشهٔ بخش‌های بالا باز کنید. برای شرایط دقیق به سرفصل رسمی درس مراجعه کنید.

Every statistics course begins with a shared vocabulary, because the same word can mean something quite specific in statistics even…

Statistics often begins by describing what could happen in a defined situation. Before summarizing results, we need to be clear about…

Statistics begins with information collected about people, objects, or events. Before summarizing that information, identify what was…

Probability describes how likely an event is. An event is an outcome, or group of outcomes, that interests us, such as a spinner…

Statistics begins by asking who or what the data describe and how those data were gathered. A population is the full group a question…

A probability describes how likely an event is. It is a number from 0 to 1: 0 means the event cannot occur, and 1 means it is…

Qualitative data describe qualities or group membership rather than measured amounts. Examples include a person’s preferred type of…

Sometimes a question asks for the chance that two events both occur. For example, a student might ask for the chance that two items…

Organize, display, summarize, and interpret qualitative and quantitative data.

• 1.1 · Use basic statistical terms and notation (published written lesson)
• 1.2 · Classify variables and types of data (published written lesson)
• 1.3 · Distinguish populations, samples, experiments, and summation notation (published written lesson)
• 1.4 · Organize and graph qualitative data (published written lesson)
• 1.5 · Organize and graph quantitative data (published written lesson)
• 1.6 · Calculate and interpret measures of centre for ungrouped data (published written lesson)
• 1.7 · Calculate and interpret dispersion for ungrouped data (published written lesson)
• 1.8 · Estimate the mean, variance, and standard deviation for grouped data (published written lesson)
• 1.9 · Use standard deviation to describe and compare data (published written lesson)
• 1.10 · Use measures of position and box plots (published written lesson)

Model chance processes with sample spaces, probability rules, and counting methods.

• 2.1 · Describe experiments, outcomes, events, and sample spaces (published written lesson)
• 2.2 · Compare classical, empirical, and subjective probability (published written lesson)
• 2.3 · Calculate marginal and conditional probabilities (published written lesson)
• 2.4 · Find intersections using the multiplication rule (published written lesson)
• 2.5 · Find unions using the addition rule (published written lesson)
• 2.6 · Use counting rules, factorials, and combinations (published written lesson)

Work with discrete random variables, binomial models, and normal distributions.

• 3.1 · Build probability distributions for discrete random variables (written lesson not published)
• 3.2 · Find the mean and standard deviation of a discrete random variable (written lesson not published)
• 3.3 · Recognize and solve binomial probability problems (written lesson not published)
• 3.4 · Use the standard normal distribution and z-scores (written lesson not published)
• 3.5 · Solve probability problems with normal distributions (written lesson not published)
• 3.6 · Approximate binomial probabilities with a normal distribution (written lesson not published)

Use sampling distributions, confidence intervals, and hypothesis tests for one population.

• 4.1 · Find the mean and standard deviation of the sample-mean distribution (written lesson not published)
• 4.2 · Determine the shape of the sample-mean distribution (written lesson not published)
• 4.3 · Use the sampling distribution of a sample proportion (written lesson not published)
• 4.4 · Construct a confidence interval for a mean when population standard deviation is known (written lesson not published)
• 4.5 · Construct a confidence interval for a mean when population standard deviation is unknown (written lesson not published)
• 4.6 · Construct a large-sample confidence interval for a population proportion (written lesson not published)
• 4.7 · Test a population mean when population standard deviation is known (written lesson not published)
• 4.8 · Test a population mean when population standard deviation is unknown (written lesson not published)
• 4.9 · Test a population proportion with a large sample (written lesson not published)

Compare means, proportions, variances, distributions, and several group means.

• 5.1 · Compare two independent means when population standard deviations are known (written lesson not published)
• 5.2 · Compare two independent means when population standard deviations are unknown but equal (written lesson not published)
• 5.3 · Compare two means using paired data (written lesson not published)
• 5.4 · Compare two population proportions (written lesson not published)
• 5.5 · Perform a chi-square goodness-of-fit test (written lesson not published)
• 5.6 · Test independence or homogeneity with a contingency table (written lesson not published)
• 5.7 · Make inferences about a population variance (written lesson not published)
• 5.8 · Compare several population means using one-way analysis of variance (written lesson not published)

Describe and assess linear relationships using regression and correlation.

• 6.1 · Fit and interpret a simple linear regression model (written lesson not published)
• 6.2 · Interpret residual standard deviation and the coefficient of determination (written lesson not published)
• 6.3 · Make inferences about the simple linear regression slope (written lesson not published)
• 6.4 · Calculate and interpret linear correlation (written lesson not published)
• 6.5 · Apply correlation and regression while recognizing their limitations (written lesson not published)

Find the sample mean of 4, 7, 7, 10, and 12.

Worked method: The sum is 40 and n = 5, so x̄ = 40/5 = 8. In context, the sample average is 8 units.

Of 80 students, 32 study online; 20 of those online students work full time. Find P(full time | online).

Worked method: Restrict the denominator to online students: 20/32 = 0.625. Thus 62.5% of the online students in this sample work full time.

A 95% confidence interval for a population mean is (18.2, 21.6). Interpret it.

Worked method: Using this method, we are 95% confident that the population mean lies between 18.2 and 21.6. The statement concerns the unknown population mean, not 95% of individual observations.

A fair die is rolled once. Find the probability of an even result.

A z-score is 1.25. Is the observation above or below the mean, and by how many standard deviations?