4.1 Statistics and probability - SL content

Objective notes

12 learning objectives

—SL 4.1—Sampling and data

• Understand population, sample, random sample, discrete and continuous data.

• Assess reliability, bias, missing data, recording errors and outliers.

• Use simple random, convenience, systematic, quota and stratified sampling.

—SL 4.2—Data presentation

• Use frequency tables, histograms and cumulative frequency graphs.

• Find median, quartiles, percentiles, range and IQR.

• Produce and compare box-and-whisker diagrams; mark outliers.

—SL 4.3—Summary statistics

• Use mean, median, mode, modal class and grouped-data mean estimates.

• Use IQR, standard deviation and variance; technology may calculate SD/variance.

• Understand effects of adding/subtracting or scaling all data values.

—SL 4.4—Correlation and regression

• Use scatter diagrams, lines of best fit and Pearson correlation coefficient r.

• Distinguish positive/negative/zero and strong/weak/no correlation.

• Correlation does not imply causation; use regression line for prediction with caution.

—SL 4.5—Probability basics

• Use trial, outcome, sample space, event and relative frequency.

• Calculate P(A)=n(A)/n(U), complements and expected number of occurrences.

• Represent sample spaces with lists or tables.

—SL 4.6—Combined, conditional and independent events

• Use Venn, tree, sample-space diagrams and outcome tables.

• Use P(A union B)=P(A)+P(B)-P(A intersection B).

• Use conditional probability and independence, with/without replacement.

—SL 4.7—Discrete random variables

• Understand discrete random variables and probability distributions.

• Find expected value/mean; interpret E(X)=0 as a fair game context.

—SL 4.8—Binomial distribution

• Use binomial distribution as an appropriate model.

• Use mean and variance of binomial distribution.

• Use technology for binomial probabilities; formal proofs are not required.

—SL 4.9—Normal distribution

• Use normal distribution curve and its properties.

• Use 68-95-99.7 rule around mean and standard deviation.

• Use technology for normal and inverse-normal probabilities.

—SL 4.10—Regression x on y

• Use equation of regression line of x on y for prediction.

• Know prediction direction matters; an x-on-y line is not always reliable for predicting y from x.

—SL 4.11—Formal conditional probability

• Use P(A|B)=P(A intersection B)/P(B).

• Use P(A intersection B)=P(B)P(A|B).

• Test for independence using conditional probability.

—SL 4.12—Standardizing normal variables

• Standardize normal variables using z-values.

• z-value measures number of standard deviations from the mean.

• Use z-values to find unknown means and standard deviations.