IB Maths: Applications and Interpretation chapter 4: Statistics and probability MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

71 exam-style questions on Statistics and probability, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

71 questions · 8 topics · 10 per test

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What chapter 4 covers

Ten Statistics and probability questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. A test at the 5% significance level gives a p-value of 0.032. What is the correct conclusion?

  1. A
    Do not reject H0, since 0.032 < 0.05
  2. B
    Reject H0, since 0.032 > 0.01
  3. C
    Reject H0, since 0.032 < 0.05
  4. D
    Do not reject H0, since the p-value is positive
Show answer

Answer: C. If the p-value is less than the significance level, the result is significant and H0 is rejected.

2. A data set has mean 20 and standard deviation 4. Every value is multiplied by 1.5 and then 2 is added. Find the new mean and variance.

  1. A
    mean 32, variance 24
  2. B
    mean 32, variance 36
  3. C
    mean 30, variance 36
  4. D
    mean 32, variance 38
Show answer

Answer: B. New mean = 1.5 × 20 + 2 = 32. The standard deviation becomes 1.5 × 4 = 6, so the variance is 36; adding 2 does not change the spread.

3. A and B are independent events with P(A) = 0.3 and P(B) = 0.5. Find P(A ∪ B).

  1. A
    0.80
  2. B
    0.15
  3. C
    0.65
  4. D
    0.50
Show answer

Answer: C. Independent: P(A ∩ B) = 0.3 × 0.5 = 0.15. Then P(A ∪ B) = 0.3 + 0.5 − 0.15 = 0.65. 0.80 treats them as mutually exclusive.

4. A coach claims a new diet increases the mean sprint speed of athletes. Which alternative hypothesis should be tested?

  1. A
    H1: μnew ≠ μold
  2. B
    H1: μnew = μold
  3. C
    H1: μnew > μold
  4. D
    H1: μnew < μold
Show answer

Answer: C. The claim is in one direction (an increase), so a one-tailed test with μnew > μold is used. Equality belongs in H0.

5. A line of best fit drawn by eye on a scatter diagram should pass through which point?

  1. A
    the origin
  2. B
    the first and last data points
  3. C
    the point with the largest x value
  4. D
    the mean point, (mean of x, mean of y)
Show answer

Answer: D. The regression line always passes through the mean point, so a line of best fit by eye should too. It need not pass through the origin.

6. In a contingency table with grand total 200, a cell has row total 80 and column total 50. Find its expected frequency under the null hypothesis.

  1. A
    40
  2. B
    20
  3. C
    25
  4. D
    16
Show answer

Answer: B. Expected = row total × column total ÷ grand total = 80 × 50 ÷ 200 = 20.

7. 2% of people have a disease. A test is positive for 95% of people with the disease and for 8% of people without it. A person tests positive. Find the probability they have the disease.

  1. A
    0.950
  2. B
    0.0974
  3. C
    0.0190
  4. D
    0.195
Show answer

Answer: D. P(positive) = 0.02 × 0.95 + 0.98 × 0.08 = 0.0974, so P(disease | positive) = 0.019 ÷ 0.0974 = 0.195. 0.950 is P(positive | disease), the reverse condition.

8. Which of these variables is continuous?

  1. A
    the number of goals scored in a match
  2. B
    a shoe size
  3. C
    the number of siblings a student has
  4. D
    the time taken to run 100 m
Show answer

Answer: D. Time is measured and can take any value in a range, so it is continuous. Goals and siblings are counted, and shoe sizes only take set values, so they are discrete.

9. A game costs $2 to play. A player receives $10 with probability 0.15 and nothing otherwise. Find the player's expected gain per game.

  1. A
    $1.50
  2. B
    $0.50
  3. C
    −$2.00
  4. D
    −$0.50
Show answer

Answer: D. Expected winnings = 10 × 0.15 = $1.50, and subtracting the $2 cost gives −$0.50, so the game is not fair to the player. $1.50 forgets the cost.

10. P(X = x) = kx for x = 1, 2, 3, 4. Find E(X).

  1. A
    3
  2. B
    2.5
  3. C
    0.1
  4. D
    30
Show answer

Answer: A. k(1 + 2 + 3 + 4) = 1 gives k = 0.1. E(X) = 0.1(1 + 4 + 9 + 16) = 3. 0.1 is k, not the expected value.

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Ways to practise this chapter

Statistics and probability: questions students ask

How many Statistics and probability MCQs are there?

71, each with the answer and a short explanation, across 8 topics: SL4.1 Collecting data and sampling, SL4.2 Presenting data: histograms, cumulative frequency and box plots, SL4.3 Measures of central tendency and dispersion, SL4.4, SL4.10 Correlation and regression, SL4.5, SL4.6 Probability: Venn diagrams, tree diagrams and conditional probability, SL4.7, SL4.8 Discrete random variables and the binomial distribution, SL4.9 The normal distribution, SL4.11 Hypothesis testing: χ² and t-tests. Every chapter test draws ten of them, so you can take it many times.

Is the IB Maths: Applications and Interpretation chapter 4 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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