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Mathematics Applications & Interpretation (AI)

SL 4.10-Spearman’s rank correlation coefficient

Which Correlation Coefficient Is More Resistant to Outliers?

Learn why Spearman’s rank correlation coefficient is more resistant to outliers than Pearson’s r, with an IB Math AI comparison and exam guidance.

SL 4.9-Normal distribution

What Percentage of Data Falls Within 1, 2, and 3 Standard Deviations of the Mean?

Learn the 68-95-99.7 empirical rule for normal distributions, how to interpret standard-deviation intervals, and how IB Math AI tests this concept.

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SL 4.11-Expected, observed, hypotheses, chi squared, gof, t-test

What's the Difference Between the Null Hypothesis and Alternative Hypothesis?

Learn how null and alternative hypotheses differ in IB Math AI SL 4.11, with examples, decision rules, misconceptions, and clear exam technique.

SL 4.11-Expected, observed, hypotheses, chi squared, gof, t-test

What Are Degrees of Freedom in a Chi-Squared Test?

Learn what degrees of freedom means in IB Math AI chi-squared tests, how to calculate it for independence and goodness-of-fit, and avoid common exam errors.

SL 4.10-Spearman’s rank correlation coefficient

How Does Spearman's Coefficient Handle Non-Linear (Monotonic) Relationships?

Learn how Spearman's coefficient measures non-linear monotonic relationships using ranks, handles ties, and differs from Pearson's correlation in IB exams.

SL 4.11-Expected, observed, hypotheses, chi squared, gof, t-test

What Is a Significance Level and a p-Value?

Understand significance levels and p-values in IB Math AI SL hypothesis tests, including decision rules, a worked example, and exam mistakes to avoid.

SL 4.11-Expected, observed, hypotheses, chi squared, gof, t-test

How Do You Perform a Chi-Squared Goodness of Fit Test?

Learn the IB Math AI chi-squared goodness of fit test: hypotheses, expected frequencies, GDC calculation, degrees of freedom, and conclusion.

SL 4.11-Expected, observed, hypotheses, chi squared, gof, t-test

How Do You Perform a T-Test to Compare the Means of Two Populations?

Learn the IB Math AI SL method for a pooled two-sample t-test: hypotheses, GDC setup, p-value comparison, assumptions, and exam conclusions.

SL 4.11-Expected, observed, hypotheses, chi squared, gof, t-test

How Do You Perform a Chi-Squared Test for Independence Using a Contingency Table?

Learn the IB Math AI method for a chi-squared independence test: hypotheses, expected frequencies, degrees of freedom, p-value, and conclusion.

SL 4.11-Expected, observed, hypotheses, chi squared, gof, t-test

What's the Difference Between a One-Tailed and Two-Tailed Test?

Learn how one-tailed and two-tailed hypothesis tests differ, how the alternative hypothesis determines the tail, and how to conclude in IB Math AI.

AHL 4.12-Data collection, reliability and validity tests

How Do You Design a Valid Survey or Questionnaire?

Learn how to design a valid survey or questionnaire for IB Math AI HL, including sampling, unbiased wording, response options, validity, and reliability.

AHL 4.12-Data collection, reliability and validity tests

What's the Difference Between Test-Retest Reliability and Parallel Forms Reliability?

Learn how test-retest and parallel forms reliability differ in IB Math AI HL, including their procedures, purposes, limitations, and exam use.

AHL 4.12-Data collection, reliability and validity tests

How Do Reliability and Validity Differ in Data Collection?

Learn how reliability differs from validity in IB Math AI data collection, with examples, improvement methods, misconceptions, and exam advice.

AHL 4.12-Data collection, reliability and validity tests

What's the Difference Between Content Validity and Criterion-Related Validity?

Compare content validity with criterion-related validity, including construct coverage, external benchmarks, misconceptions and IB Math AI HL exam technique.

AHL 4.13-Non-linear regression

What Is the Sum of Square Residuals and How Does It Measure Model Fit?

Learn how squared residuals are summed, why a lower total indicates closer model fit, and how IB Math AI HL students compare regression models correctly.

AHL 4.12-Data collection, reliability and validity tests

How Do You Choose Appropriate Categories for a Chi-Squared Table?

Learn how to choose mutually exclusive, exhaustive and meaningful categories for an IB Math AI chi-squared table, with expected frequencies above 5.

AHL 4.13-Non-linear regression

How Do You Fit a Non-Linear Regression Curve Using Technology?

Learn the IB Math AI HL method for fitting quadratic, cubic, exponential, power and sine regressions with a GDC and evaluating model fit in exams.

AHL 4.13-Non-linear regression

What Is the Coefficient of Determination (R²) and What Does It Tell You?

Learn how R² measures variation explained by a regression model, how to interpret it, and what IB Math AI exam responses must include.

AHL 4.14-Linear transformation of a single RV, E(X) and VAR(X), unbiased estimators

How Does a Linear Transformation Affect the Expected Value and Variance of a Random Variable?

Learn how transforming a random variable by Y = aX + b changes its expected value, variance, and standard deviation in IB Math AI HL exams.

AHL 4.13-Non-linear regression

Why Isn't R² Alone a Good Way to Choose Between Different Models?

Learn why R² cannot select the best regression model alone and how IB Math AI students should assess residuals, context, domain, fit, and validity.

AHL 4.14-Linear transformation of a single RV, E(X) and VAR(X), unbiased estimators

What Is an Unbiased Estimator of the Population Mean and Variance?

Learn why the sample mean and corrected sample variance are unbiased estimators of population mean and variance for IB Math AI HL exams with clear formulas.

AHL 4.15-Central limit theorem

What Is the Central Limit Theorem?

Learn the central limit theorem for IB Math AI HL, including sample-mean distributions, a worked GDC example, assumptions, and common exam errors.

AHL 4.14-Linear transformation of a single RV, E(X) and VAR(X), unbiased estimators

Why Does Sample Variance Divide by n or n - 1?

Learn why variance divides by n for a complete data set but by n-1 for an unbiased sample estimate, including GDC notation and IB exam guidance at HL.

AHL 4.16-Confidence intervals

How Do You Calculate a Confidence Interval for a Population Mean?

Learn how to calculate and interpret a confidence interval for a population mean in IB Math AI HL using z or t intervals, GDC setup, and exam wording.

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