Mathematics: Applications and Interpretation HL

Statistics and probability

Official Mathematics: applications and interpretation HL strand for the current first-assessment-2021 syllabus.

Calculate states from transition matrices Develop calculate states from transition matrices through finite, checked AI HL practice aligned to current syllabus point AIHL 4.19. Calculate Spearman rank correlation Develop calculate spearman rank correlation through finite, checked AI HL practice aligned to current syllabus point AIHL 4.10. Interpret chi-square tests for independence Develop interpret chi-square tests for independence through finite, checked AI HL practice aligned to current syllabus point AIHL 4.11. Construct confidence intervals for means Develop construct confidence intervals for means through finite, checked AI HL practice aligned to current syllabus point AIHL 4.16. Test population means with normal models Develop test population means with normal models through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Find steady states of Markov chains Develop find steady states of markov chains through finite, checked AI HL practice aligned to current syllabus point AIHL 4.19. Calculate expected values of discrete distributions Develop calculate expected values of discrete distributions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.7. Calculate Poisson point probabilities Develop calculate poisson point probabilities through finite, checked AI HL practice aligned to current syllabus point AIHL 4.17. Calculate sample-mean parameters using the central limit theorem Develop calculate sample-mean parameters using the central limit theorem through finite, checked AI HL practice aligned to current syllabus point AIHL 4.15. Calculate reverse conditional probabilities from trees Develop calculate reverse conditional probabilities from trees through finite, checked AI HL practice aligned to current syllabus point AIHL 4.6. Combine expectations and variances of independent variables Develop combine expectations and variances of independent variables through finite, checked AI HL practice aligned to current syllabus point AIHL 4.14. Calculate unbiased sample variance from population variance Develop calculate unbiased sample variance from population variance through finite, checked AI HL practice aligned to current syllabus point AIHL 4.14. Calculate sums of squared residuals Develop calculate sums of squared residuals through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13. Interpret coefficients of determination Develop interpret coefficients of determination through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13. Standardize normal observations Develop standardize normal observations through finite, checked AI HL practice aligned to current syllabus point AIHL 4.9. Interpret p-values and significance Develop interpret p-values and significance through finite, checked AI HL practice aligned to current syllabus point AIHL 4.11. Interpret Type I and Type II errors Develop interpret type i and type ii errors through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Test a normal mean when variance is unknown Develop test a normal mean when variance is unknown through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Test matched-pair mean differences Develop test matched-pair mean differences through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Interpret confidence intervals for means Develop interpret confidence intervals for means through finite, checked AI HL practice aligned to current syllabus point AIHL 4.16. Distinguish reliability from validity Develop distinguish reliability from validity through finite, checked AI HL practice aligned to current syllabus point AIHL 4.12. Interpret linear regression parameters Develop interpret linear regression parameters through finite, checked AI HL practice aligned to current syllabus point AIHL 4.4. Classify predictions from regression models Develop classify predictions from regression models through finite, checked AI HL practice aligned to current syllabus point AIHL 4.4. Select relevant variables for investigations Develop select relevant variables for investigations through finite, checked AI HL practice aligned to current syllabus point AIHL 4.12. Calculate exact binomial probabilities Develop calculate exact binomial probabilities through finite, checked AI HL practice aligned to current syllabus point AIHL 4.8. Calculate cumulative binomial probabilities Develop calculate cumulative binomial probabilities through finite, checked AI HL practice aligned to current syllabus point AIHL 4.8. Calculate binomial means and variances Develop calculate binomial means and variances through finite, checked AI HL practice aligned to current syllabus point AIHL 4.8. Calculate expected monetary values Develop calculate expected monetary values through finite, checked AI HL practice aligned to current syllabus point AIHL 4.7. Calculate expected values from probability trees Develop calculate expected values from probability trees through finite, checked AI HL practice aligned to current syllabus point AIHL 4.7. Assess Poisson model assumptions Develop assess poisson model assumptions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.17. Combine independent Poisson variables Develop combine independent poisson variables through finite, checked AI HL practice aligned to current syllabus point AIHL 4.17. Find normal percentiles using technology Develop find normal percentiles using technology through finite, checked AI HL practice aligned to current syllabus point AIHL 4.9. Interpret inverse-normal output Develop interpret inverse-normal output through finite, checked AI HL practice aligned to current syllabus point AIHL 4.9. Interpret Pearson correlation and causation Develop interpret pearson correlation and causation through finite, checked AI HL practice aligned to current syllabus point AIHL 4.4. Select nonlinear regression models Develop select nonlinear regression models through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13. Calculate standard deviation from summaries Develop calculate standard deviation from summaries through finite, checked AI HL practice aligned to current syllabus point AIHL 4.2. Construct confidence intervals when variance is unknown Develop construct confidence intervals when variance is unknown through finite, checked AI HL practice aligned to current syllabus point AIHL 4.16. Improve biased survey questions Develop improve biased survey questions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.12. Calculate probabilities of unions Develop calculate probabilities of unions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.6. Combine mutually exclusive tree paths Develop combine mutually exclusive tree paths through finite, checked AI HL practice aligned to current syllabus point AIHL 4.6. Calculate conditional probabilities from tables Develop calculate conditional probabilities from tables through finite, checked AI HL practice aligned to current syllabus point AIHL 4.6. Transform expected values Develop transform expected values through finite, checked AI HL practice aligned to current syllabus point AIHL 4.14. Transform variances Develop transform variances through finite, checked AI HL practice aligned to current syllabus point AIHL 4.14. Combine independent normal variables Develop combine independent normal variables through finite, checked AI HL practice aligned to current syllabus point AIHL 4.15. Construct upper binomial critical regions Develop construct upper binomial critical regions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Calculate binomial Type I errors Develop calculate binomial type i errors through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Calculate expected chi-square frequencies Develop calculate expected chi-square frequencies through finite, checked AI HL practice aligned to current syllabus point AIHL 4.11. Calculate chi-square goodness-of-fit statistics Develop calculate chi-square goodness-of-fit statistics through finite, checked AI HL practice aligned to current syllabus point AIHL 4.11. Construct z confidence intervals for means Develop construct z confidence intervals for means through finite, checked AI HL practice aligned to current syllabus point AIHL 4.16. Conduct binomial proportion tests Develop conduct binomial proportion tests through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Select lower binomial critical regions Develop select lower binomial critical regions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Calculate binomial Type II errors Develop calculate binomial type ii errors through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Interpret Spearman technology output Develop interpret spearman technology output through finite, checked AI HL practice aligned to current syllabus point AIHL 4.10. Diagnose regression residual patterns Develop diagnose regression residual patterns through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13. Calculate Poisson interval probabilities Develop calculate poisson interval probabilities through finite, checked AI HL practice aligned to current syllabus point AIHL 4.17. Calculate upper-tail Poisson probabilities Develop calculate upper-tail poisson probabilities through finite, checked AI HL practice aligned to current syllabus point AIHL 4.17. Construct normal critical boundaries with known variance Develop construct normal critical boundaries with known variance through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Calculate one-tailed Poisson test p-values Develop calculate one-tailed poisson test p-values through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Calculate normal mean test statistics with known variance Develop calculate normal mean test statistics with known variance through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Conclude correlation tests from technology output Develop conclude correlation tests from technology output through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Distinguish correlation significance from strength Develop distinguish correlation significance from strength through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Interpret one-tailed Poisson test output Develop interpret one-tailed poisson test output through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18. Select nonlinear model families from data structure Develop select nonlinear model families from data structure through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13. Evaluate limitations of high coefficients of determination Develop evaluate limitations of high coefficients of determination through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13. Calculate residuals from nonlinear models Develop calculate residuals from nonlinear models through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13. Compare fitted models using fit and context Develop compare fitted models using fit and context through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13. Interpret parameters in exponential models Develop interpret parameters in exponential models through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13. Three-state Markov chains and long-term behaviour Use column-stochastic transition matrices to calculate finite-step, steady-state, calibrated, and convergence behaviour.