Statistics Practice Questions
A-Levels · A-Level Mathematics · 136 free MCQs with instant results and detailed explanations.
136
Total
43
Easy
72
Medium
21
Hard
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Sample Questions from Statistics
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
What is the mean of the following data set: 4, 8, 6, 5, 3?
A.
5.2
B.
5.5
C.
6
D.
4.5
Show Answer & Explanation
Correct Answer: A
To find the mean, sum all values (4 + 8 + 6 + 5 + 3 = 26) and divide by the number of values (5). Thus, mean = 26 / 5 = 5.2.
Q2
Easy
If a dataset has a median of 15, what can be inferred about the data?
A.
Half of the data points are below 15.
B.
All data points are below 15.
C.
The mean is also 15.
D.
Data points are all identical.
Show Answer & Explanation
Correct Answer: A
The median is the middle value in a sorted dataset. Thus, half of the data points will be less than or equal to the median value, which is 15.
Q3
Easy
In a normal distribution, which of the following statements is true?
A.
The mean is always greater than the median.
B.
The distribution is symmetrical about the mean.
C.
The mode is less than the mean.
D.
All three measures of central tendency are always equal.
Show Answer & Explanation
Correct Answer: B
In a normal distribution, the data is evenly distributed around the mean, leading to symmetry. This means the mean, median, and mode are all equal; however, the key point is the symmetry about the mean.
Q4
Medium
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random, what is the probability that it is not blue?
A.
0.7
B.
0.6
C.
0.5
D.
0.3
Show Answer & Explanation
Correct Answer: A
The total number of balls is 10 (5 red + 3 blue + 2 green). The number of non-blue balls is 7 (5 red + 2 green). Therefore, the probability of drawing a non-blue ball is 7/10 = 0.7.
Q5
Medium
The mean of a dataset is 20 and the variance is 4. What is the standard deviation of this dataset?
A.
2
B.
4
C.
20
D.
16
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Correct Answer: A
The standard deviation is the square root of the variance. Since the variance is 4, the standard deviation is √4 = 2.
Q6
Medium
In a normal distribution, if the mean is 50 and the standard deviation is 5, within what range do approximately 68% of the data lie?
A.
45 to 55
B.
40 to 60
C.
50 to 70
D.
30 to 80
Show Answer & Explanation
Correct Answer: A
In a normal distribution, about 68% of the data falls within one standard deviation of the mean. Therefore, the range is from 50 - 5 to 50 + 5, which is 45 to 55.
Q7
Medium
A dataset has the following values: 8, 10, 12, 14, 16. What is the median of this dataset?
A.
12
B.
10
C.
14
D.
16
Show Answer & Explanation
Correct Answer: A
To find the median, arrange the data in ascending order. The middle value of the sorted data set (8, 10, 12, 14, 16) is 12.
Q8
Hard
In a certain dataset, the mean is 50 and the standard deviation is 5. If 80% of the data falls within which range according to the Empirical Rule?
A.
45 to 55
B.
40 to 60
C.
30 to 70
D.
50 to 70
Show Answer & Explanation
Correct Answer: A
According to the Empirical Rule, approximately 68% of data falls within one standard deviation of the mean, and about 95% falls within two standard deviations. Here, one standard deviation from the mean (50) gives the range of 45 to 55, which contains around 68% of the data. However, for 80%, we need to ensure it falls within a tighter range, which is still best represented by 45 to 55.
Q9
Hard
A researcher is analyzing the correlation between study hours and exam scores in a sample of students. If the correlation coefficient is found to be 0.85, what does this imply about the relationship between the two variables?
A.
There is a strong positive relationship.
B.
There is a weak negative relationship.
C.
There is no relationship.
D.
There is a strong negative relationship.
Show Answer & Explanation
Correct Answer: A
A correlation coefficient of 0.85 indicates a strong positive relationship between study hours and exam scores. This means that as study hours increase, the exam scores tend to increase as well.
Q10
Hard
A dataset contains the following values: 5, 7, 8, 12, 15, 18, 20. What is the median of this dataset?
A.
10
B.
12
C.
11
D.
13
Show Answer & Explanation
Correct Answer: B
To find the median, we must first arrange the data in ascending order, which is already done here: 5, 7, 8, 12, 15, 18, 20. Since there are 7 values (an odd number), the median is the middle value. The middle value in this ordered list is the 4th value, which is 12. Therefore, the median of the dataset is 12, making option B the correct answer.
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Statistics — A-Levels A-Level Mathematics Practice Questions Online
This page contains 136 practice MCQs for the chapter Statistics in A-Levels A-Level Mathematics. The questions are organized by difficulty — 43 easy, 72 medium, 21 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.