Statistics and Probability Practice Questions
IB (International Baccalaureate) · IB Math AA HL · 146 free MCQs with instant results and detailed explanations.
146
Total
53
Easy
71
Medium
22
Hard
Start Practicing Statistics and Probability
Take a timed quiz or customize your practice session
Sample Questions from Statistics and Probability
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
What is the median of the following data set: 3, 7, 5, 9, 1?
A.
5
B.
6
C.
7
D.
9
Show Answer & Explanation
Correct Answer: A
To find the median, the data set must be arranged in ascending order: 1, 3, 5, 7, 9. The median is the middle number, which is 5.
Q2
Easy
If the probability of an event occurring is 0.25, what is the probability of it not occurring?
A.
0.25
B.
0.50
C.
0.75
D.
1.00
Show Answer & Explanation
Correct Answer: C
The probability of an event not occurring is calculated as 1 minus the probability of the event occurring. Thus, 1 - 0.25 = 0.75.
Q3
Easy
What is the median of the following set of numbers: 3, 7, 5, 9, 1?
A.
5
B.
6
C.
7
D.
4
Show Answer & Explanation
Correct Answer: A
To find the median, first arrange the numbers in ascending order: 1, 3, 5, 7, 9. The median is the middle number, which is 5.
Q4
Medium
In a normal distribution, if the mean is 50 and the standard deviation is 5, what is the z-score of a value of 60?
A.
1
B.
2
C.
1.5
D.
0.5
Show Answer & Explanation
Correct Answer: B
The z-score is calculated as (X - mean) / standard deviation. For X=60, z = (60-50)/5 = 10/5 = 2.
Q5
Medium
A survey of students' study hours per week showed a mean of 15 hours and a standard deviation of 3 hours. If the data is normally distributed, what percentage of students study between 12 and 18 hours?
A.
68%
B.
95%
C.
99.7%
D.
50%
Show Answer & Explanation
Correct Answer: A
Using the empirical rule, approximately 68% of data falls within one standard deviation of the mean in a normal distribution. The range 12-18 hours includes 1 standard deviation from the mean of 15.
Q6
Medium
If the correlation coefficient between two variables X and Y is -0.8, what can be inferred about the relationship between these variables?
A.
There is a strong positive relationship
B.
There is a weak negative relationship
C.
There is a strong negative relationship
D.
There is no relationship
Show Answer & Explanation
Correct Answer: C
A correlation coefficient of -0.8 indicates a strong negative relationship between the two variables. As one variable increases, the other variable tends to decrease.
Q7
Medium
A dataset has the following five values: 2, 4, 6, 8, 10. What is the standard deviation of this dataset?
A.
2.83
B.
3.16
C.
2.24
D.
1.58
Show Answer & Explanation
Correct Answer: A
The standard deviation is calculated using the formula for a sample: sqrt((ฮฃ(x - xฬ)ยฒ) / (n - 1)). Here, the mean (xฬ) is 6, and the calculations yield a standard deviation of approximately 2.83.
Q8
Hard
In a bag of 20 marbles, 12 are red, 5 are blue, and 3 are green. If two marbles are drawn at random without replacement, what is the probability that both marbles drawn are of the same color?
A.
0.5
B.
0.45
C.
0.4
D.
0.3
Show Answer & Explanation
Correct Answer: B
The probability of drawing two marbles of the same color can be calculated by finding the probability for each color and summing them. For red, P(RR) = (12/20) * (11/19); for blue, P(BB) = (5/20) * (4/19); for green, P(GG) = (3/20) * (2/19). Summing gives approximately 0.45.
Q9
Hard
A dataset has a mean of 50 and a standard deviation of 5. If the distribution is approximately normal, what is the probability that a randomly selected value from this dataset will be greater than 60?
A.
0.1587
B.
0.0228
C.
0.8413
D.
0.5000
Show Answer & Explanation
Correct Answer: B
To find the probability of a value greater than 60, we first calculate the z-score: z = (60 - 50) / 5 = 2. The probability corresponding to z = 2 in the standard normal distribution table is approximately 0.9772. Hence, the probability of a value greater than 60 is 1 - 0.9772 = 0.0228.
Q10
Hard
In a group of students, the probability that a student studies Mathematics is 0.6, and the probability that a student studies Physics is 0.4. If the events are independent, what is the probability that a student studies both Mathematics and Physics?
A.
0.24
B.
0.60
C.
0.40
D.
0.10
Show Answer & Explanation
Correct Answer: A
Since the events are independent, the probability of both events occurring is the product of their individual probabilities: P(Mathematics โฉ Physics) = P(Mathematics) * P(Physics) = 0.6 * 0.4 = 0.24.
Showing 10 of 146 questions. Start a quiz to practice all questions with scoring and timer.
Practice All 146 Questions →More IB Math AA HL Chapters
Other IB (International Baccalaureate) Subjects
Statistics and Probability โ IB (International Baccalaureate) IB Math AA HL Practice Questions Online
This page contains 146 practice MCQs for the chapter Statistics and Probability in IB (International Baccalaureate) IB Math AA HL. The questions are organized by difficulty โ 53 easy, 71 medium, 22 hard โ so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.