IB Mathematics Applications & Interpretation Statistics and Probability

Question Type 1: Given some worded scenario of real-life data collection, outlining the characteristics of the data and possible problems

Question Type 1: Constructing histograms given the frequency distribution table

Question Type 2: Constructing cumilative frequency graphs given the frequency distribution table

Question Type 3: Finding the quartiles using the cumulative frequency graph

Question Type 4: Interpretating information from box and whisker plots

Question Type 5: Constructing box and whisker plots using cumulative frequency graphs or tables

Question Type 6: Finding missing values in a box and whisker plot using given information

Question Type 7: Comparing two different data sets of box and whiskers

Question Type 1: Given some values for data, finding each: mean, mode, median and range

Question Type 2: Data given as parameters and finding the value of the data given some relationship/values of the central tendancy

Question Type 3: Given a frequency table, calculating the mean, median, modal class and range of the data

Question Type 4: Finding the value of the frequency of a specific class with some condition on mean, median or mode

Question Type 5: Given a data set, finding the value of the standard deviation, variance and IQR

Question Type 6: Given values of a specific data set and some characteristics, being able to find the similar values for another data set

Question Type 7: Determining the effect on mean, mode, median, range, variance, standard deviation and IQR given specific transformations of data

Question Type 1: Calculating the Pearsons moment-correlation coefficient r for a bivariate data set

Question Type 2: Calculating the linear relationship between the data in the form y=ax+b

Question Type 3: Forecasting another value given a linear fit

Question Type 4: Using bivariate data to plot scatter diagrams

Question Type 5: Describing the correlation

Question Type 1: Creating sample spaces for different experiments

Question Type 2: Finding the set of outcomes under a given event for different experiments

Question Type 3: Using simple events to calculate probabilities

Question Type 4: Finding expected occurrences using probable outcomes

Question Type 1: Constructing Venn diagrams to calculate probabilities for 2 events

Question Type 2: Constructing Venn diagrams to calculate probabilities for 3 or more events

Question Type 3: Given a worded problem, converting to a tree diagram to calculate probability of an outcome

Question Type 4: Creating a table of outcomes to calculate probabilities of two different random events cojoint into one

Question Type 5: Working with conditions

Question Type 6: Working with replacement

Question Type 7: Given values of events, using diagrams to interpret probabilities

Question Type 1: Finding the probability of certain outcomes of random variables

Question Type 2: Finding the expected value of outcomes of random variables

Question Type 3: Finding certain values of parameters such that the probability table holds true

Question Type 1: Finding the probability of outcomes for binomial distribution using the GDC

Question Type 2: Finding the expected value and variance for a binomially distributed variable

Question Type 3: Using n and p as parameters and finding what values of either satisfy some conditions

Question Type 1: Using properties of normal distribution to find probabilities given some value

Question Type 2: Finding the interval for which a specific percentage of data is concentrated

Question Type 3: Finding the probability values of normally distributed variables

Question Type 4: Finding the value of X using inverse normal

Question Type 1: Creating rank tables for a given data set

Question Type 2: Finding the Spearman's Rank Coefficient using rank tables

Question Type 3: Using parameter or algebraic forms of data when calculating with rank tables

Question Type 4: Calculating correlation coefficients with and without outliers

AHL 4.10.b Understanding outliers

Question Type 1: Formulating test hypothesis for different types of tests

Question Type 2: Finding the p-value or critical value given the other for a specific distribution

Question Type 3: Initiating the chi-squared independence test with the hypothesis and critical regions

Question Type 4: Finding the table of expected frequencies for a chi-squared independence test

Question Type 5: Calculating the chi-squared value and/or p-value to conclude the chi-squared independence test

Question Type 6: Initiating the chi-squared goodness of fit test with the hypothesis and critical region

Question Type 7: Finding expected frequencies for a chi-squared goodness of fit test

Question Type 8: Calculating the chi-squared value and/or the p-value to conclude the chi-squared goodness of fit test

Question Type 9: Initiating the one sample t-test with the hypothesis and critical region

Question Type 10: Calculating the t-statistics for one sample t-tests

Question Type 11: Calculating critical value and/or p-value to conclude the one sample t-test

Question Type 12: Initiating the two sample t-test with the hypothesis and critical region

Question Type 13: Determining the type of two sample t-test and calculating the according t-statistic

Question Type 14: Calculating the critical value and/or p-value to conclude the two sample t-test

Question Type 15: Performing and entire statistical test

Question Type 1: Assessing the quality of questioning

Question Type 2: Fixing the line of questioning for poor questions

Question Type 3: Identifying the appropriate variables for a given contextual information

Question Type 4: Choosing the appropriate data given contextual information

Question Type 5: Categorizing data to ensure a specific expected frequency

Question Type 6: Performing the chi-squared test for data categorization such that the expected frequency is at least 5

Question Type 7: Determining the degree of freedom for chi-squared goodness of fit tests

Question Type 8: Finding degree of freedom and performing chi-squared goodness of fit test

Question Type 9: Determining whether certain issues pertain to validity or reliability

Question Type 10: Determining the type of reliability

Question Type 11: Determining the type of validity

Question Type 1: Determining best fit model for a given set of data

Question Type 2: Determining the fit of a model for a given data set and a specific given model

Question Type 3: Comparing two different models over the same data using SSR

Question Type 4: Determining the R^2 value for different models on a set of data

Question Type 5: Connecting pearson's correlation coefficient and determination for linear model with or without parameters

Question Type 1: Finding the expected value or variance of a transformed variable given some information on its summary statistics

Question Type 2: Finding the expected value or variance of a transformed linear combination of multiple variables given some information on their joint summary statistics

Question Type 3: Estimating the mean and variance using unbiased estimators

Question Type 4: Working with parameters in determining unbiased estimators

Question Type 1: Finding the distribution of a linear combination of independent normal variables

Question Type 2: Finding the distribution of the sample mean using CLT

Question Type 3: Solving probability questions of other distributions using CLT

Question Type 1: Finding the mean for a given set of data and distribution with known variance

Question Type 2: Finding the confidence interval for a given set of data and distribution for unknown variance

Question Type 3: Solving for the value of some parameters given the confidence interval

Question Type 1: Choosing the correct distribution for a given context

Question Type 2: Finding the probability of some event given some contextual information of a poisson distribution

Question Type 3: Calculating with a linear combination of independent poisson distributions

Question Type 4: Solving word problems involving multiple poisson distributions

Question Type 1: Performing a hypothesis test for the mean given the variance for single sample

Question Type 2: Performing a hypothesis test for the mean with unknown variance of a single sample

Question Type 3: Performing a hypothesis test comparing two means of unpaired samples with equal variances

Question Type 4: Performing a hypothesis test comparing two means for paired samples

Question Type 5: Performing a hypothesis test on single proportion using the binomial distribution

Question Type 6: Performing a hypothesis test on population mean using the poisson distribution

Question Type 7: Performing a hypothesis test on population mean using the normal approximation of a poisson distribution

Question Type 8: Performing a hypothesis test for correlation under bivariate normality

Question Type 9: Finding the critical region under a poisson on binomial distribution

Question Type 10: Calculating the probability of a type 1 error under a critical region for a binomial or poisson distribution

Question Type 11: Calculating the probability of a type II error for a critical region under poisson on binomial distribution

Question Type 1: Construction transition matrices from diagrams or context descriptions

Question Type 2: Creating state diagrams

Question Type 3: Using Markov chains to model real-world processes

Question Type 4: Calculating powers of transition matrices

Question Type 5: Determining steady-state distributions and their interpretation