IB Maths AA: Statistics and probability — Practice Questions & Answers
A complete tour of IB Mathematics AA Topic 4 (SL and HL): collecting and sampling data, summarising it with measures of centre and spread including standard deviation, handling grouped data with cumulative frequency and box plots, analysing bivariate data through correlation and least-squares regression, and the full probability toolkit from conditional probability and independence to tree and Venn diagrams, discrete random variables, expected value, and the binomial and normal distributions.
50 practice questions available for this topic — here are 10 with full answers and explanations.
A school of 1200 students is divided into year groups, and a researcher selects a number of students from each year group in proportion to its size. Which sampling method is this?
Stratified sampling
Simple random sampling
Convenience sampling
Systematic sampling
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WhyDividing the population into groups (strata) and sampling in proportion to each group's size is stratified sampling.
2Multiple choice · Easy
Find the mean of the data set $4, 7, 7, 10, 12$.
$8$
$7$
$10$
$40$
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WhyThe sum is $40$ and there are $5$ values, so the mean is $\frac{40}{5}=8$.
3Multiple choice · Easy
For the data set $3, 5, 8, 8, 11, 14$, what is the median?
$8$
$8.17$
$9.5$
$11$
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WhyWith $6$ values, the median is the mean of the $3$rd and $4$th values: $\frac{8+8}{2}=8$.
4Multiple choice · Easy
A fair six-sided die is rolled once. What is the probability of obtaining a number greater than $4$?
$\frac{1}{3}$
$\frac{1}{2}$
$\frac{2}{3}$
$\frac{1}{6}$
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WhyThe outcomes greater than $4$ are $5$ and $6$, giving $\frac{2}{6}=\frac{1}{3}$.
5Multiple choice · Easy
What is the range of the data set $12, 5, 9, 20, 7$?
$15$
$20$
$9$
$13$
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WhyThe range is the largest value minus the smallest value: $20-5=15$.
6Multiple choice · Easy
A random variable follows $X\sim B(n,p)$. What does the parameter $n$ represent?
The number of trials
The probability of success
The expected number of successes
The variance
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WhyIn the binomial distribution $X\sim B(n,p)$, $n$ is the number of independent trials and $p$ is the probability of success on each trial.
7Multiple choice · Easy
Two events $A$ and $B$ are mutually exclusive. Which statement is always true?
$P(A\cap B)=0$
$P(A\cup B)=0$
$P(A)\times P(B)=0$
$P(A|B)=P(A)$
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WhyMutually exclusive events cannot occur together, so $P(A\cap B)=0$.
8Multiple choice · Easy
On a cumulative frequency graph for $80$ data values, the median is read off at which cumulative frequency?
$40$
$20$
$60$
$80$
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WhyThe median corresponds to the middle of the data, read at a cumulative frequency of $\frac{80}{2}=40$.
9Multiple choice · Easy
A Pearson correlation coefficient of $r=-0.92$ indicates which type of linear relationship?
Strong negative
Strong positive
Weak negative
No correlation
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WhyA value close to $-1$ indicates a strong negative linear correlation between the variables.
10Multiple choice · Medium
The frequency table shows: value $2$ (frequency $3$), value $4$ (frequency $5$), value $6$ (frequency $2$). What is the mean?
$3.8$
$4$
$12.67$
$3.33$
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WhyThe mean is $\frac{2\times 3+4\times 5+6\times 2}{3+5+2}=\frac{6+20+12}{10}=\frac{38}{10}=3.8$.
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