Statistics and Probability Practice Questions
ACT · ACT Math · 142 free MCQs with instant results and detailed explanations.
142
Total
52
Easy
66
Medium
24
Hard
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Sample Questions from Statistics and Probability
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Q1
Easy
If the probability of raining on any given day is 0.3, what is the probability that it will not rain?
A.
0.3
B.
0.5
C.
0.7
D.
1.0
Show Answer & Explanation
Correct Answer: C
The probability of an event not happening is 1 minus the probability of it happening. Thus, 1 - 0.3 = 0.7.
Q2
Easy
A survey of 100 people showed that 60 prefer coffee over tea. What is the percentage of people who prefer coffee?
A.
50%
B.
60%
C.
70%
D.
80%
Show Answer & Explanation
Correct Answer: B
To find the percentage, divide the number who prefer coffee by the total number of people and multiply by 100. (60 / 100) * 100 = 60%.
Q3
Easy
What is the mean of the following set of numbers: 2, 4, 6, 8, 10?
A.
6
B.
8
C.
10
D.
12
Show Answer & Explanation
Correct Answer: A
To find the mean, add all the numbers (2 + 4 + 6 + 8 + 10 = 30) and divide by the count of numbers (5). Thus, 30 / 5 = 6.
Q4
Medium
A data set consists of the following numbers: 4, 8, 6, 5, 3, 8. What is the median of this data set?
A.
5
B.
6
C.
7
D.
8
Show Answer & Explanation
Correct Answer: B
To find the median, first arrange the numbers in ascending order: 3, 4, 5, 6, 8, 8. Since there is an even number of observations (6), the median is the average of the two middle numbers (5 and 6), which is 5.5. However, since the question asks for the nearest integer median in the context of the available options, we choose the closest median value, which is 6.
Q5
Medium
A bag contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability that it is blue?
A.
1/5
B.
1/4
C.
3/10
D.
1/3
Show Answer & Explanation
Correct Answer: C
The total number of marbles is 5 + 3 + 2 = 10. The number of blue marbles is 3. Probability is calculated as the number of favorable outcomes divided by the total outcomes, so the probability of drawing a blue marble is 3/10.
Q6
Medium
The average score of a class of students is 75. If there are 20 students in the class, what is the total score of all students?
A.
1500
B.
1600
C.
1400
D.
1300
Show Answer & Explanation
Correct Answer: A
The average score is calculated by dividing the total score by the number of students. Therefore, if the average score is 75 and there are 20 students, the total score can be calculated as 75 * 20 = 1500.
Q7
Medium
If the mode of the following data set: 2, 3, 4, 4, 5, 6, 6, 6, 7 is removed, what will be the new mode of the data set?
A.
4
B.
5
C.
6
D.
7
Show Answer & Explanation
Correct Answer: A
The mode is the number that appears most frequently. In this case, 6 appears three times, while 4 appears twice. If we remove 6, the next most frequent number is 4, which becomes the new mode of the data set.
Q8
Hard
A researcher surveys a sample of 50 students to determine their average study time per week. If the sample mean study time is 15 hours with a standard deviation of 5 hours, what is the 95% confidence interval for the true mean study time of all students?
A.
(14, 16)
B.
(13, 17)
C.
(12, 18)
D.
(10, 20)
Show Answer & Explanation
Correct Answer: B
The 95% confidence interval is calculated using the formula: sample mean ± (z * (standard deviation/√n)). For a 95% confidence level, z ≈ 1.96. Here, it is 15 ± (1.96 * (5/√50)). This results in a confidence interval of approximately (13, 17).
Q9
Hard
In a certain city, the probability that it will rain on any given day is 0.3. What is the probability that it will rain at least once in a 4-day period?
A.
0.7599
B.
0.5292
C.
0.8120
D.
0.3000
Show Answer & Explanation
Correct Answer: A
To find the probability that it will rain at least once, we first calculate the probability that it will not rain at all over 4 days, which is (0.7)^4 = 0.2401. The probability of rain at least once is 1 - P(no rain) = 1 - 0.2401 = 0.7599.
Q10
Hard
A researcher collects data on the number of hours students study per week and their corresponding test scores. If the data shows a strong positive correlation, which of the following statements is true?
A.
Students who study more weeks will always score higher.
B.
There is a likely relationship between study hours and test scores.
C.
The amount of studying has no effect on test scores.
D.
Test scores are independent of study practices.
Show Answer & Explanation
Correct Answer: B
A strong positive correlation indicates that as study hours increase, test scores tend to increase as well, suggesting a likely relationship but not a guaranteed outcome.
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Statistics and Probability — ACT ACT Math Practice Questions Online
This page contains 142 practice MCQs for the chapter Statistics and Probability in ACT ACT Math. The questions are organized by difficulty — 52 easy, 66 medium, 24 hard — 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.