IB Maths AI 4.3 Definitions

This page contains our IB Maths AI definitions for 4.3. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Distribution properties'.

All Topic 4 Sub-topics 4.1: Fundamentals Of Statistics 4.2: Visualising Statistics 4.3: Distribution Properties 4.4: Introduction To Linear Statistics 4.5: Probability 4.6: Probability Distributions 4.7: Hypotheses & Tests (HL)4.8: Data collection & categorisation (HL)4.9: Advanced linear statistics (HL)4.10: Linear transformations & combinations (HL)4.11: Confidence intervals (HL)4.12: Poisson distribution (HL)4.13: Distribution tests (HL)4.14: Transition matrices

dispersion

The extent to which data values vary about a central value, quantified using measures such as interquartile range, standard deviation, and variance.

interquartile range

Measures the spread of the middle

50\%

of an ordered data set, calculated as the difference between the upper and lower quartiles:

IQR=Q_3-Q_1

mean

The expected value of a random variable; if $X \sim \mathrm{Poisson}(\lambda)$ , then $E(X) = \lambda$

population

The full set of all possible values of interest, described by parameters such as the mean '

\mu

' and variance '

\sigma^2

quartiles

Values that split ordered data into four equal parts; on a cumulative frequency graph with $n$ values, they are estimated at cumulative frequencies $\frac{n}{4}$ and $\frac{3n}{4}$ .

spread

How dispersed the data values are, described using measures of dispersion such as interquartile range, standard deviation, and variance.

standard deviation

The square root of the variance,

\sigma=\sqrt{\mathrm{Var}(X)}

, giving spread in the same units as the random variable.

variance

Measures spread using the mean of squared distances from the mean, so values far from the mean have greater influence; measured in squared units and equal to the square of the standard deviation.

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