FortyFive › Revision notes › IB Maths: Analysis & Approaches › IB Maths: Analysis & Approaches: Statistics and probability
Data, regression, probability, binomial and normal distributions. 14 subtopics.
In this topic: 4.1 · 4.2 · 4.3 · 4.4 · 4.5 · 4.6 · 4.7 · 4.8 · 4.9 · 4.10 · 4.11 · 4.12 · 4.13 · 4.14
Population: everyone of interest. Sample: the part you actually measure.
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Frequency tables and histograms (equal class widths at SL).
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Centre: mean, median, mode (modal class for grouped data). Spread: range, IQR, standard deviation \(\sigma\) (use your GDC).
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Pearson's \(r\) lies between \(-1\) and \(1\). Values close to \(\pm1\) show strong linear correlation.
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Relative frequency estimates probability from experiments.
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Use Venn diagrams, tree diagrams and sample space diagrams.
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A game is fair if the expected gain is 0.
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Conditions: fixed number of trials, two outcomes, constant probability, independent trials.
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Bell-shaped and symmetric about \(\mu\); mean = median = mode.
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To predict \(x\) from a given value of \(y\), use the regression line of \(x\) on \(y\).
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P(A\mid B)=\frac{P(A\cap B)}{P(B)}\qquad A,B\text{ independent}\iff P(A\mid B)=P(A)
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\(z\) tells you how many standard deviations a value is from the mean.
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A tree diagram makes Bayes questions much easier.
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The mode of a continuous random variable is where \(f(x)\) is greatest.
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