Statistics Quizzes for Year 11 Comprehensive School Students

Question 1

A market researcher surveys 100 customers to find out their favorite coffee shop chain. Which statistical test should the researcher use to determine the most popular coffee shop chain?

Accepted Answer

Chi-squared test of independence

Answer

One-sample t-test

Answer

Two-sample t-test

Answer

Correlation analysis

Question 2

Which potential drawback is associated with stratified sampling?

Accepted Answer

Increased time and cost compared to other methods

Answer

Ensuring fair representation of subgroups

Answer

Reducing sampling bias

Answer

Ease of implementation

Question 3

What is statistical significance, and why is it important in hypothesis testing?

Accepted Answer

The probability of observing a result as extreme or more extreme than the one obtained, assuming the null hypothesis is true.

Answer

The closeness of a sample statistic to the population parameter.

Answer

A predetermined level set by the researcher to reject the null hypothesis.

Answer

Irrelevant to hypothesis testing.

Question 4

Which sampling method is most likely to produce biased results in statistical research?

Accepted Answer

Quota sampling

Answer

Random sampling

Answer

Cluster sampling

Answer

Snowball sampling

Question 5

What is a key feature of a representative sample?

Accepted Answer

It reflects the variety of the population it represents.

Answer

It is a random selection from the population.

Answer

It is always larger than the population it represents.

Answer

It favors a specific subgroup of the population.

Question 6

In statistical studies involving human participants, what are the ethical principles of informed consent and data protection?

Accepted Answer

Informed consent means giving participants enough information about the study and getting their permission to take part.

Answer

Researchers should collect data without participants' knowledge to save time.

Answer

Researchers don't have to keep participants' data confidential.

Question 7

Which of the following is a measure of dispersion?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 8

Which of the following is a characteristic of random sampling?

Accepted Answer

Every individual in the population has an equal chance of being selected

Answer

The sample is selected based on convenience

Answer

The sample is divided into strata to ensure representation of different subgroups

Answer

The sample is selected systematically

Question 9

In a significance test, the null hypothesis is accepted at a significance level of 0.01. What does this imply?

Accepted Answer

There is a 99% probability that the null hypothesis is true

Answer

There is a 1% probability that the null hypothesis is false

Answer

There is a 1% probability that the alternative hypothesis is true

Answer

There is a 99% probability that the alternative hypothesis is false

Question 10

Which type of regression analysis is used to predict the value of a categorical dependent variable from one or more independent variables?

Accepted Answer

Logistic regression

Answer

Linear regression

Answer

Spearman's rank correlation

Answer

Kendall's tau correlation

Question 11

What is the y-intercept of the regression line?

Accepted Answer

The point where the line intercepts the y-axis

Answer

The point where the line intercepts the x-axis

Answer

The slope of the line

Answer

The correlation coefficient

Question 12

Which measure of central tendency represents the value that appears most often in a data set?

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Range

Question 13

In a typical bell-shaped distribution, approximately what percentage of data falls within one standard deviation of the mean?

Accepted Answer

68%

Answer

34%

Answer

95%

Answer

99%

Question 14

Which measure of dispersion is most appropriate for a data set with a skewed distribution?

Accepted Answer

Interquartile range

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 15

What is the key distinction between a population and a sample?

Accepted Answer

A population represents the entire group of interest, while a sample is a subset of that group.

Answer

A sample represents the entire group of interest, while a population is a subset of that group.

Answer

A population is a hypothetical group, while a sample is a real group.

Answer

There is no difference between a population and a sample.

Question 16

What is the primary use of a scatter plot?

Accepted Answer

To illustrate the relationship between two variables.

Answer

To compare the means of two data sets.

Answer

To identify outliers.

Answer

To make predictions.

Question 17

Which measure of central tendency represents the "middle" value of a data set?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 18

Calculate the interquartile range (IQR) of the following data set: 5, 7, 9, 11, 13, 15, 17.

Accepted Answer

6

Answer

4

Answer

8

Answer

10

Question 19

A histogram is a graphical representation of a data set that displays the:

Accepted Answer

Frequency of data values in specific intervals

Answer

Cumulative frequency of data values

Answer

Mean and median of the data set

Answer

Standard deviation of the data set

Question 20

Given a data set with a mean of 10 and a variance of 4, what is the standard deviation?

Accepted Answer

4

Answer

2

Answer

8

Answer

16

Question 21

A scatter plot is used to illustrate the:

Accepted Answer

Relationship between two variables

Answer

Distribution of data

Answer

Mean and standard deviation of a data set

Answer

Correlation coefficient between two variables

Question 22

Which measure of association indicates the strength and direction of a linear relationship?

Accepted Answer

Correlation coefficient

Answer

Regression line

Answer

Mean

Answer

Median

Question 23

What is the primary purpose of a hypothesis test?

Accepted Answer

Determine if there is a significant difference between two data sets

Answer

Make predictions about future data

Answer

Identify outliers in a data set

Answer

Calculate the probability of an event

Question 24

In a hypothesis test, the p-value represents the:

Accepted Answer

Probability of rejecting the null hypothesis when it is true

Answer

Probability of accepting the null hypothesis when it is false

Answer

Difference between the sample mean and the hypothesized mean

Answer

Number of standard deviations from the mean

Question 25

Which of the following is the best measure of variability?

Accepted Answer

Standard deviation

Answer

Range

Answer

Variance

Answer

Mean absolute deviation

Question 26

Which of the following can be used to compare the variability of two data sets?

Accepted Answer

Coefficient of variation

Answer

Standard deviation

Answer

Z-score

Answer

Correlation coefficient

Question 27

Identify the measure of central tendency that represents the average of all data points.

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 28

Which data visualization method is most suitable for displaying the distribution of values within a data set?

Accepted Answer

Histogram

Answer

Bar chart

Answer

Scatter plot

Answer

Line graph

Question 29

Calculate the mean of the following data set: 4, 6, 8, 10, 12.

Accepted Answer

8

Answer

6

Answer

10

Answer

12

Question 30

Which of the following is not a measure of dispersion?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 31

A data set with a high standard deviation is considered to be:

Accepted Answer

Widely spread

Answer

Narrowly concentrated

Answer

Symmetrically distributed

Answer

Normally distributed

Question 32

Which sampling method involves selecting a representative group from a population through a random process?

Accepted Answer

Random sampling

Answer

Systematic sampling

Answer

Stratified sampling

Answer

Cluster sampling

Question 33

Which statistical test is used to compare the means of two independent groups?

Accepted Answer

t-test

Answer

ANOVA

Answer

Chi-square test

Answer

Regression analysis

Question 34

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

Accepted Answer

Standard Deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 35

Which of the following describes a measure that represents the typical or central value of a dataset?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Range

Answer

Quartile

Question 36

Which formula calculates the mean, or average, of a set of numerical values?

Accepted Answer

Sum of values divided by the number of values

Answer

Median value minus minimum value

Answer

Maximum value plus minimum value divided by 2

Answer

(Quartile 1 plus Quartile 3) divided by 2

Question 37

Which formula calculates the standard deviation, a measure of spread in a dataset?

Accepted Answer

Square root of the variance

Answer

Sum of values divided by the number of values

Answer

Median value minus minimum value

Answer

Maximum value plus minimum value divided by 2

Question 38

What is the primary purpose of conducting a hypothesis test?

Accepted Answer

To determine if there is a statistically significant difference between two or more groups.

Answer

To estimate the population mean.

Answer

To predict future values of a variable.

Answer

To validate a theory.

Question 39

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

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 40

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

Accepted Answer

A population is the entire set of data, while a sample is a subset of the population

Answer

A sample is the entire set of data, while a population is a subset of the sample

Answer

A population is a group of people, while a sample is all the data

Answer

A sample is a group of people, while a population is all the data

Question 41

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

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 42

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

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 43

To explore the connection between study time and final exam results, a researcher collects data on both factors for a group of students. Which graph type is best for showing this relationship?

Accepted Answer

Scatter plot

Answer

Bar chart

Answer

Histogram

Question 44

Which value appears most frequently in the data set: 5, 7, 9, 11, 9, 13, 9?

Accepted Answer

9

Answer

5

Answer

11

Answer

13

Question 45

Which measure of central tendency is appropriate for skewed data, where extreme values may distort the mean?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 46

Which of the following is a measure of the strength and direction of the relationship between two variables?

Accepted Answer

Correlation coefficient

Answer

Regression coefficient

Answer

Standard deviation

Answer

Variance

Question 47

A scatter plot shows a negative correlation between two variables. What does this indicate?

Accepted Answer

As the value of one variable increases, the value of the other variable decreases.

Answer

As the value of one variable increases, the value of the other variable also increases.

Answer

There is no relationship between the two variables.

Answer

The two variables are inversely proportional.

Question 48

Which of the following types of data is considered qualitative?

Accepted Answer

Gender

Answer

Age

Answer

Height

Answer

Income

Question 49

A box plot shows a median of 10 and an interquartile range of 4. What is the value of the upper quartile?

Accepted Answer

14

Answer

12

Answer

16

Answer

18

Question 50

Which of the following measures does NOT summarize the data around its central value?

Accepted Answer

Correlation coefficient

Answer

Mean

Answer

Median

Answer

Mode

Question 51

A dataset has a mean of 10 and a standard deviation of 2. What is the z-score of a value of 14 in this dataset?

Accepted Answer

1

Answer

-2

Answer

0

Answer

2

Question 52

Which of the following graphs is best suited to display categorical data?

Accepted Answer

Pie chart

Answer

Histogram

Answer

Bar chart

Answer

Scatterplot

Question 53

A survey reveals that 60% of individuals prefer tea over coffee. What is the probability of randomly selecting someone who prefers coffee?

Accepted Answer

0.4

Answer

0.5

Answer

0.6

Answer

0.7

Question 54

Which of the following is the primary function of standard deviation?

Accepted Answer

Summarizing the spread of data

Answer

Comparing different datasets

Answer

Making predictions about future outcomes

Answer

Determining the probability of an event occurring

Question 55

A scatterplot shows a positive correlation. What does this indicate?

Accepted Answer

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

Answer

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

Answer

There is no relationship between the variables.

Answer

The variables are negatively correlated.

Question 56

Which of the following is a method used to calculate the median of a dataset?

Accepted Answer

Arranging the data in ascending order and finding the middle value

Answer

Adding all the values in the dataset and dividing by the number of values

Answer

Finding the mean and standard deviation of the dataset

Answer

Using a statistical calculator

Question 57

A confidence interval is constructed with a 95% confidence level. What does this imply?

Accepted Answer

There is a 95% chance that the true population parameter is within the interval.

Answer

There is a 5% chance that the true population parameter is outside the interval.

Answer

There is a 95% chance that the sample mean is equal to the population mean.

Answer

There is a 5% chance that the population standard deviation is outside the interval.

Question 58

Which of the following is a measure that describes the typical value of a data set?

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Correlation

Question 59

Which of the following sampling methods involves randomly selecting individuals from a population?

Accepted Answer

Random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Answer

Convenience sampling

Question 60

A correlation coefficient of -0.8 indicates:

Accepted Answer

A strong negative relationship

Answer

A strong positive relationship

Answer

A weak positive relationship

Answer

A weak negative relationship

Question 61

Which of the following is NOT a measure of typical value in a data set?

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Mode

Question 62

The standard deviation is a measure of:

Accepted Answer

The spread of data around the mean

Answer

The average value of a data set

Answer

The difference between the maximum and minimum values

Answer

The number of times a value occurs in a data set

Question 63

Which statistical measure is least affected by extreme values (outliers)?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 64

A correlation coefficient of -1 indicates:

Accepted Answer

A strong negative relationship

Answer

A strong positive relationship

Answer

No relationship between variables

Answer

A weak negative relationship