Master Statistics and Probability: Interactive Quizzes for Eighth Graders

Question 1

To test if sunflowers in a region are taller than 100 cm on average, researchers conduct a hypothesis test. List the key steps in the correct order.

Accepted Answer

Formulate hypotheses, collect data, calculate test statistic and p-value, draw conclusion

Answer

Collect data, formulate hypotheses, draw conclusion, calculate test statistic and p-value

Answer

Calculate test statistic and p-value, formulate hypotheses, collect data, draw conclusion

Answer

Draw conclusion, calculate test statistic and p-value, formulate hypotheses, collect data

Question 2

In a research project, you've gathered data on students' weekly video game hours and their GPAs. Explain how you'll use technology to analyze this data and draw conclusions about their relationship.

Accepted Answer

Create a scatter plot, regression line, and hypothesis test to examine the correlation and statistical significance.

Answer

Calculate mean and standard deviation for both variables and compare them for a relationship.

Answer

Use a pie chart for video game time and a bar graph for GPA to show distributions.

Answer

Create a histogram for video game time and a box plot for GPA to show frequency and distribution.

Question 3

The standard deviation of a data set provides information about its:

Accepted Answer

Spread

Answer

Center

Answer

Shape

Answer

Correlation

Question 4

In a dataset, which measure of central tendency represents the value that occurs most frequently?

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Range

Question 5

Which of the following is NOT a measure of central tendency that describes the typical value of a dataset?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 6

A class collected data on their test scores. Which probability distribution would most likely represent this data?

Accepted Answer

Normal Distribution

Answer

Binomial Distribution

Answer

Poisson Distribution

Answer

Uniform Distribution

Question 7

The mean of a dataset is 10 and the median is 12. Which of the following could be true about the data?

Accepted Answer

The data is skewed to the right, meaning it has more values above the mean.

Answer

The data is skewed to the left, meaning it has more values below the mean.

Answer

The data is symmetric, meaning it is evenly distributed around the mean.

Answer

The data is bimodal, meaning it has two distinct peaks.

Question 8

A coin is flipped twice. What is the probability of getting two heads?

Accepted Answer

1/4

Answer

1/2

Answer

3/4

Answer

1

Question 9

Which of the following is NOT an ethical consideration when collecting and using data?

Accepted Answer

Selling data to third parties without their knowledge or consent

Answer

Protecting the privacy of individuals

Answer

Using data responsibly and not misrepresenting it

Answer

Obtaining informed consent from participants before collecting their data

Question 10

Which measure of central tendency is highly influenced by extreme values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Standard Deviation

Question 11

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn randomly without replacement, what is the likelihood of drawing both green marbles?

Accepted Answer

1/36

Answer

1/20

Answer

1/15

Answer

1/10

Question 12

A box-and-whisker plot shows a median of 25, a lower quartile of 15, and an upper quartile of 35. What is the range of this dataset?

Accepted Answer

15

Answer

5

Answer

10

Answer

20

Question 13

A histogram displays the distribution of test scores in a class. The histogram exhibits a right-skewed shape. What does this indicate about the distribution?

Accepted Answer

A majority of scores are higher than the mean.

Answer

A majority of scores are lower than the mean.

Answer

The distribution is bell-shaped.

Answer

The distribution is uniform.

Question 14

In a class of 25 students, the average test score was 78%. If the teacher generously adds 5 points to each student's score, what will be the new average score?

Accepted Answer

88%

Answer

78%

Answer

83%

Answer

93%

Question 15

Consider a fair six-sided die. What is the probability of rolling a number greater than 3?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/6

Question 16

The median of a data set is the middle value when arranged in order. Which of the following is NOT a characteristic of the median?

Accepted Answer

It is always the same as the mean.

Answer

It is not affected by outliers.

Answer

It can be a decimal.

Answer

It can be found for both even and odd-numbered data sets.

Question 17

A scatter plot shows a positive correlation between study hours and test scores. What does this indicate?

Accepted Answer

As study hours increase, test scores tend to increase.

Answer

As study hours decrease, test scores tend to increase.

Answer

There is no relationship between study hours and test scores.

Answer

Test scores decrease as study hours increase.

Question 18

A company claims their product can reduce task completion time by 25%. If the original average completion time was 60 minutes, what is the projected new average time?

Accepted Answer

45 minutes

Answer

30 minutes

Answer

75 minutes

Answer

90 minutes

Question 19

Which of the following is NOT a measure of central tendency?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Mode

Answer

Median

Question 20

A survey asks participants: "What is your favorite color?" What type of data is the survey collecting?

Accepted Answer

Qualitative data

Answer

Quantitative data

Answer

Discrete data

Answer

Continuous data

Question 21

A data set contains the following values: 2, 4, 4, 6, 8. Which value is the mode?

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 22

If a fair six-sided die is rolled, what is the probability of rolling an even number?

Accepted Answer

1/4

Answer

1/3

Answer

1/6

Answer

1/8

Question 23

Which of the following is a type of probability distribution that is bell-shaped and symmetrical?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Skewness distribution

Answer

Poisson distribution

Question 24

Which of the following is a graphical representation of a data set that shows the distribution of data points along two axes?

Accepted Answer

Scatterplot

Answer

Histogram

Answer

Bar graph

Answer

Pie chart

Question 25

Which of the following factors influences the spread or variability of a data set?

Accepted Answer

Dispersion

Answer

Central tendency

Answer

Skewness

Answer

Outliers

Question 26

Which of the following measures represents the typical value of a data set?

Accepted Answer

Mean: The average of all the values in a data set.

Answer

Median: The middle value of a data set when arranged in ascending order.

Answer

Mode: The value that appears most frequently in a data set.

Answer

Range: The difference between the highest and lowest values in a data set.

Question 27

A data set has the following values: 2, 4, 6, 8, 10. What is the median of the data set?

Accepted Answer

4: The middle value when the data is arranged in ascending order.

Answer

5: The average of the middle two values.

Answer

6: The most common value.

Answer

7: The sum of all the values.

Question 28

A statistical study found that people who exercise regularly are less likely to develop heart disease. Which of the following is the most likely conclusion from this study?

Accepted Answer

Exercise is related to a reduced risk of heart disease.

Answer

Exercise causes heart disease.

Answer

Heart disease causes exercise.

Answer

There is no relationship between exercise and heart disease.

Question 29

Which probability distribution is used to model the number of successes in a series of independent experiments, where each experiment has a constant probability of success?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Exponential distribution

Question 30

Which of the following is not a measure of central tendency used to describe a set of numerical data?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 31

Which probability distribution models the number of successes in a sequence of independent experiments, each with a constant probability of success?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Uniform distribution

Question 32

When a fair coin is tossed twice, what is the probability of getting heads on both tosses?

Accepted Answer

1/8

Answer

1/2

Answer

1/4

Answer

1/16

Question 33

Which of the following is **NOT** a measure of central tendency?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 34

Which of the following graphs best represents a normal distribution?

Accepted Answer

A bell-shaped curve

Answer

A straight line

Answer

A parabola

Answer

A circle

Question 35

Which of the following is a characteristic of a standard normal distribution?

Accepted Answer

Mean of 0 and standard deviation of 1

Answer

Mean of 1 and standard deviation of 0

Answer

Mean of 0 and standard deviation of 2

Answer

Mean of 1 and standard deviation of 2

Question 36

Which type of graph is best suited for displaying the distribution of a continuous dataset?

Accepted Answer

Histogram

Answer

Bar graph

Answer

Pie chart

Answer

Scatter plot

Question 37

What is the difference between a sample and a population in statistics?

Accepted Answer

A sample is a subset of the population.

Answer

A population is a subset of the sample.

Answer

A sample is always smaller than the population.

Answer

A population is always larger than the sample.

Question 38

What is the difference between a discrete and a continuous probability distribution?

Accepted Answer

A discrete distribution takes on only specific values, while a continuous distribution takes on any value within a range.

Answer

A continuous distribution takes on only specific values, while a discrete distribution takes on any value within a range.

Answer

A discrete distribution is always symmetric, while a continuous distribution is always skewed.

Answer

A continuous distribution is always symmetric, while a discrete distribution is always skewed.

Question 39

What is the difference between correlation and causation?

Accepted Answer

Correlation measures the strength and direction of a linear relationship between two variables, while causation measures the cause-and-effect relationship between two variables.

Answer

Causation measures the strength and direction of a linear relationship between two variables, while correlation measures the cause-and-effect relationship between two variables.

Answer

Correlation and causation are the same thing.

Answer

Correlation and causation are unrelated.

Question 40

Which of the following is a measure of the central value of a data set?

Accepted Answer

Mean

Answer

Variance

Answer

Standard deviation

Answer

Range

Question 41

What is the probability of rolling a 6 on a fair six-sided die?

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 42

Which of the following is NOT a common type of statistical graph?

Accepted Answer

Trigonometric function graph

Answer

Bar graph

Answer

Scatterplot

Answer

Pie chart

Question 43

Which graphical representation is most appropriate for displaying the distribution of a set of continuous data?

Accepted Answer

Histogram

Answer

Scatter plot

Answer

Pie chart

Answer

Bar graph

Question 44

A bag contains 6 red balls, 4 blue balls, and 2 yellow balls. If you draw a ball without replacement, what is the probability of drawing a yellow ball?

Accepted Answer

1/6

Answer

1/4

Answer

1/3

Question 45

Which measure describes how data is spread out?

Accepted Answer

Standard deviation

Answer

Median

Answer

Mean

Answer

Mode

Question 46

What is the probability of obtaining a '6' when rolling a standard six-sided die?

Accepted Answer

1/6

Answer

1/4

Answer

1/3

Question 47

In a dataset, which data point appears most frequently?

Accepted Answer

Mode

Answer

Median

Answer

Mean

Question 48

The correlation coefficient indicates:

Accepted Answer

The strength and direction of the linear relationship between two variables.

Answer

The probability of one variable influencing the other.

Answer

The mean of the two variables.

Question 49

Which sampling method ensures an equal chance of selecting any member of the population?

Accepted Answer

Simple random sampling

Answer

Convenience sampling

Answer

Cluster sampling

Question 50

The difference between the highest and lowest values in a dataset is called the:

Accepted Answer

Range

Answer

Standard deviation

Answer

Quartile deviation

Answer

Variance

Question 51

Which graphical representation illustrates the distribution of data?

Accepted Answer

Histogram

Answer

Scatterplot

Answer

Pie chart

Answer

Line plot

Question 52

What is the probability of an event not occurring?

Accepted Answer

Complement of an event

Answer

Joint probability

Answer

Union of events

Answer

Conditional probability

Question 53

In a sample space, the sum of probabilities of all outcomes is always:

Accepted Answer

1

Answer

0

Answer

Greater than 1

Answer

Less than 1

Question 54

A spinner is divided into 8 equal sections, each labeled with a different number from 1 to 8. If the spinner is spun once, what is the probability of landing on a number that is a multiple of 3?

Accepted Answer

0.375

Answer

0.5

Answer

0.25

Answer

0.125

Question 55

A scatter plot shows a positive correlation between the number of hours spent studying and test scores. Which of the following conclusions can be drawn from this data?

Accepted Answer

As study time increases, test scores tend to increase.

Answer

As study time decreases, test scores tend to increase.

Answer

There is no relationship between study time and test scores.

Question 56

Which of the following is a measure of the typical value of a statistical distribution?

Accepted Answer

Mean

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 57

What number between 0 and 1 represents the probability of an event happening?

Accepted Answer

Fraction or decimal between 0 and 1

Answer

Negative number

Answer

Integer greater than 1

Answer

Percentage less than 0

Question 58

Calculate the mean (average) of the following data set: {5, 7, 9, 11, 13}

Accepted Answer

9

Answer

11

Answer

7

Answer

13

Question 59

Which of the following graphical representations shows data values separated into intervals or categories?

Accepted Answer

Histogram

Answer

Box plot

Answer

Stem-and-leaf plot

Answer

Scatter plot

Question 60

What is the difference between a statistical population and a statistical sample?

Accepted Answer

A population is the entire group under study, while a sample is a smaller group drawn from the population.

Answer

A sample is the entire group under study, while a population is a smaller group drawn from the sample.

Answer

A population is a group of data, while a sample is a group of people.

Question 61

In a data set, which measure of central tendency represents the most frequently occurring value?

Accepted Answer

Mode

Answer

Range

Answer

Mean

Answer

Median

Question 62

What is the definition of probability in the context of an event?

Accepted Answer

A value between 0 and 1 that represents the likelihood of the event occurring

Answer

A fraction greater than 1

Answer

A number greater than 1

Answer

A negative number

Question 63

In a sample space, what is the sum of the probabilities of all possible outcomes?

Accepted Answer

1

Answer

The number of outcomes

Answer

The mean of the outcomes

Answer

0

Question 64

A bag has 5 red marbles, 3 blue marbles, and 2 green marbles. If a single marble is randomly chosen, what is the probability of selecting a blue marble?

Accepted Answer

3/10

Answer

1/10

Answer

1/2

Answer

5/10