Probability and Statistics Quizzes for Year 11 Maths

Question 1

Which of the following is NOT a key assumption of linear regression?

Accepted Answer

The data is collected from a random sample.

Answer

The relationship between the independent and dependent variables is linear.

Answer

The errors are independent and normally distributed.

Answer

The variance of the errors is constant.

Question 2

In a fair coin toss, what is the probability of landing on heads?

Accepted Answer

1 in 2

Answer

1 in 4

Answer

3 in 4

Answer

1

Question 3

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 4

The variance of a data set is 25. What is the standard deviation?

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 5

A scatter plot shows a weak negative correlation. What does this indicate?

Accepted Answer

As one variable increases, the other variable tends to decrease.

Answer

As one variable increases, the other variable tends to increase.

Answer

There is a strong relationship between the two variables.

Answer

The relationship between the two variables is non-linear.

Question 6

What is the primary purpose of using a control group in a scientific experiment?

Accepted Answer

To reduce the influence of confounding variables

Answer

To compare results to an untreated group

Answer

To replicate the experimental results

Answer

To increase the sample size

Question 7

Which of the following best describes a categorical variable?

Accepted Answer

It can be grouped into distinct categories.

Answer

It can be measured on a continuous scale.

Answer

It represents the number of occurrences in a given period.

Answer

It is the average value of a set of data.

Question 8

A correlation coefficient of 0.8 indicates:

Accepted Answer

A strong positive linear relationship

Answer

A strong negative linear relationship

Answer

A weak positive linear relationship

Answer

A weak negative linear relationship

Question 9

Which of the following measures the average value of a dataset?

Accepted Answer

Mean

Answer

Variance

Answer

Standard deviation

Answer

Range

Question 10

Which of the following is used to measure the average tendency of a dataset?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 11

Which data representation is most appropriate for displaying the distribution of test scores?

Accepted Answer

Histogram

Answer

Stem-and-leaf plot

Answer

Bar chart

Answer

Scatter plot

Question 12

Which of the following is NOT a reliable method for collecting data?

Accepted Answer

Anecdotal evidence

Answer

Surveys

Answer

Experiments

Answer

Observations

Question 13

What is the main function of a hypothesis in a statistical investigation?

Accepted Answer

Tomake a prediction

Answer

Tosummarize the findings

Answer

To confirm a theory

Answer

To prove a conclusion

Question 14

Which of the following is an example of a biased sample?

Accepted Answer

A poll of 200 adults conducted at a shopping mall.

Answer

A survey of 100 students selected randomly from a school with 500 students.

Answer

A random sample of 50 employees from a company with 200 employees.

Answer

A survey of all registered voters in a particular city.

Question 15

What is the primary purpose of a null hypothesis in statistical testing?

Accepted Answer

To demonstrate the absence of a significant difference between two groups.

Answer

To demonstrate a significant difference between two groups.

Answer

To reject the possibility of a significant difference between two groups.

Answer

To reject the possibility of no significant difference between two groups.

Question 16

Which of the following is a limitation of probability?

Accepted Answer

It cannot predict the outcome of an individual event.

Answer

It assumes that all outcomes are equally likely.

Answer

It is only applicable to large samples.

Answer

It is useless for decision-making.

Question 17

Which of the following statistical measures is used to describe the average of a dataset?

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 18

For data exhibiting a trend over time, which type of graph is most appropriate?

Accepted Answer

Line graph

Answer

Bar graph

Answer

Pie chart

Answer

Scatter plot

Question 19

A bag contains 6 red marbles, 4 blue marbles, and 2 green marbles. What is the probability of randomly drawing a blue marble?

Accepted Answer

0.33

Answer

0.2

Answer

0.5

Answer

0.6

Question 20

The standard deviation of a set of numbers is 2. If each number is multiplied by 3, what is the new standard deviation?

Accepted Answer

6

Answer

1

Answer

2

Answer

3

Question 21

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If a ball is drawn at random, what is the likelihood of drawing a red ball?

Accepted Answer

2/5

Answer

1/2

Answer

1/3

Answer

1/5

Question 22

A random sample of 50 students is taken from a population of 1000 students. The sample mean is 72 and the sample standard deviation is 10. What is the standard error of the mean?

Accepted Answer

1.41

Answer

0.2

Answer

2

Answer

10

Question 23

A scatterplot reveals a strong positive correlation between the number of hours spent studying and the test scores of students. Which interpretation is most fitting?

Accepted Answer

As the number of hours spent studying increases, test scores tend to increase.

Answer

As the number of hours spent studying increases, test scores tend to decrease.

Answer

There is no relationship between the number of hours spent studying and test scores.

Answer

The relationship between the number of hours spent studying and the test scores is weak.

Question 24

Which of the following is NOT a valid method for calculating probability?

Accepted Answer

Logical deduction

Answer

Experimental probability

Answer

Theoretical probability

Answer

Observational probability

Question 25

A survey of 100 students found that 60 preferred football. What is the sample space for this survey?

Accepted Answer

The 100 students surveyed

Answer

All students in the world

Answer

All students who prefer football

Answer

All students who do not prefer football

Question 26

Which of the following is the most appropriate graphical representation for a data set with a large number of data points?

Accepted Answer

Histogram

Answer

Bar chart

Answer

Pie chart

Answer

Scatter plot

Question 27

A scatterplot illustrates a positive correlation between two variables. Which of the following is true?

Accepted Answer

As one variable increases, the other variable tends to increase.

Answer

As one variable increases, the other variable tends to decrease.

Answer

There is no relationship between the two variables.

Answer

The variables are inversely proportional.

Question 28

What is the mean of the following data set: {10, 12, 14, 16, 18}?

Accepted Answer

14

Answer

10

Answer

12

Answer

16

Question 29

A survey of 100 students found that 60% preferred mathematics. How many students prefer mathematics?

Accepted Answer

60

Answer

40

Answer

50

Answer

70

Question 30

A hypothesis test is conducted at a significance level of 5%. The p-value is 0.04. What is the conclusion of the test?

Accepted Answer

Reject the null hypothesis

Answer

Fail to reject the null hypothesis

Answer

The data is not significant

Answer

The hypothesis is true

Question 31

A bag contains 5 blue and 3 red balls. A ball is drawn at random. What is the probability of selecting a blue ball?

Accepted Answer

5/8

Answer

1/2

Answer

3/8

Answer

1/4

Question 32

A survey of 100 students revealed that 60 preferred football, 30 preferred cricket, and 10 preferred both. How many students preferred only football or cricket?

Accepted Answer

90

Answer

80

Answer

100

Answer

110

Question 33

A box-and-whisker plot shows the following values: minimum = 5, lower quartile = 10, median = 15, upper quartile = 20, maximum = 25. What is the interquartile range?

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 34

A bag contains 3 red marbles, 2 blue marbles, and 1 green marble. One marble is drawn at random. What is the probability of drawing a blue marble?

Accepted Answer

1/3

Answer

1/6

Answer

1/2

Answer

2/3

Question 35

Which of the following is an example of a discrete random variable?

Accepted Answer

Number of siblings

Answer

Height

Answer

Age in years

Answer

Weight in kilograms

Question 36

Which of the following is not a possible value for the range of a data set?

Accepted Answer

A negative number

Answer

Zero

Answer

A decimal

Answer

A fraction

Question 37

Which of the following is not a method of data collection?

Accepted Answer

Estimation

Answer

Survey

Answer

Observation

Answer

Experiment

Question 38

A fair coin is flipped three times. What is the probability of getting at least one head?

Accepted Answer

7/8

Answer

1/8

Answer

1/2

Answer

3/4

Question 39

Which measure of central tendency is most easily affected by outliers?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 40

A bag contains 5 red balls and 3 blue balls. What is the probability of randomly selecting a red ball?

Accepted Answer

5 / 8

Answer

3 / 8

Answer

1 / 2

Answer

2 / 3

Question 41

A survey of 100 people found that 60 like coffee and 40 like tea. What is the relative frequency of people who like coffee?

Accepted Answer

0.6

Answer

0.4

Answer

0.5

Answer

0.7

Question 42

A survey was conducted to find the favorite subjects of 100 students, and the results are as follows: Mathematics (30 students), English (25 students), Science (20 students), History (15 students), Geography (10 students). What percentage of students prefer Mathematics?

Accepted Answer

30%

Answer

25%

Answer

20%

Answer

15%

Question 43

A set of data has a mean of 20 and a standard deviation of 5. According to the empirical rule, approximately what percentage of the data falls within one standard deviation of the mean? What is the range within which this data lies?

Accepted Answer

68%, 15 to 25

Answer

95%, 10 to 30

Answer

50%, 17.5 to 22.5

Answer

99.7%, 12.5 to 27.5

Question 44

In a survey of 100 people, 60 prefer tea and 40 prefer coffee. What is the relative frequency of people who prefer coffee?

Accepted Answer

0.4

Answer

0.6

Answer

0.2

Answer

0.1

Question 45

A company wants to test the effectiveness of a new advertising campaign. They randomly select 50 people to receive the new ad and another 50 people to receive the old ad. This type of sampling method is called:

Accepted Answer

Random sampling

Answer

Stratified sampling

Answer

Convenience sampling

Answer

Cluster sampling

Question 46

A box contains 5 red balls and 5 blue balls. Two balls are drawn randomly without replacement. What is the probability of drawing one red ball and one blue ball (in any order)?

Accepted Answer

1/2

Answer

3/4

Answer

1/3

Answer

1/4

Question 47

A group of students were asked to rate their satisfaction with a new school program on a scale of 1 to 5. The results are shown in the following frequency table:

| Rating | Frequency |
    |---|---|
    | 1 | 2 |
    | 2 | 5 |
    | 3 | 10 |
    | 4 | 8 |
    | 5 | 5 |

What is the mode of these ratings?

Accepted Answer

3

Answer

2

Answer

4

Answer

5

Question 48

A set of data has a range of 15 and a variance of 9. What is the standard deviation of the data?

Accepted Answer

3

Answer

15

Answer

45

Answer

9

Question 49

A group of students are randomly assigned to two different teaching methods to study a new topic. After the study period, both groups take the same test. This type of research is called:

Accepted Answer

Experimental study

Answer

Case study

Answer

Survey

Answer

Observational study

Question 50

A coin is tossed 100 times. What is the theoretical probability of getting heads?

Accepted Answer

1/2

Answer

1/100

Answer

1/4

Answer

3/4

Question 51

A survey of 100 students found that 60% of them like playing video games. How many students like playing video games?

Accepted Answer

60

Answer

100

Answer

40

Answer

80

Question 52

The range of a data set is the difference between the maximum and minimum values. What is the range of the data set {2, 4, 6, 8, 10}?

Accepted Answer

8

Answer

10

Answer

6

Answer

5

Question 53

A biased coin has a probability of 0.7 of landing on heads. What is the probability of the coin landing on tails?

Accepted Answer

0.3

Answer

0.5

Answer

0.7

Answer

1.0