Statistics Quizzes for Year 9 Maths Students in the UK

Question 1

What is the difference between the sample mean and the population mean?

Accepted Answer

The sample mean is the average of the data in a sample, while the population mean is the average of the data in the entire population.

Answer

The population mean is the average of the data in a sample, while the sample mean is the average of the data in the entire population.

Answer

The sample mean and the population mean are always the same.

Answer

The sample mean is the true average of the population, while the population mean is an estimate of the true average.

Question 2

What is a unique advantage of using stem-and-leaf plots compared to box-and-whisker plots?

Accepted Answer

Displaying individual data values

Answer

Ease of construction

Answer

Handling larger datasets

Answer

Highlighting outliers

Question 3

Consider two datasets with identical means. Explain how their standard deviations and ranges can differ. Provide an example to illustrate your explanation.

Accepted Answer

Both standard deviation and range can differ for datasets with the same mean.

Answer

Standard deviation and range are always identical for datasets with equal means.

Answer

Standard deviation can vary, but range remains constant for datasets with the same mean.

Answer

Range can vary, but standard deviation remains constant for datasets with the same mean.

Question 4

When analyzing a scatter plot to determine the relationship between two variables, which of the following methods should NOT be used?

Accepted Answer

Count the number of data points.

Answer

Examine the orientation of the points.

Answer

Draw a line of best fit.

Answer

Calculate the correlation coefficient.

Question 5

What does the mode of a dataset represent?

Accepted Answer

The most common value

Answer

The average value

Answer

The value that occurs twice

Answer

The range of values

Question 6

What does the standard deviation measure?

Accepted Answer

The average distance of data points from the mean

Answer

The most common value in a dataset

Answer

The range of values in a dataset

Answer

The sum of all data points

Question 7

In a study investigating the relationship between study time and test scores, study time is the:

Accepted Answer

Independent variable

Answer

Dependent variable

Answer

Control variable

Answer

Extraneous variable

Question 8

A data set that follows a normal distribution exhibits a:

Accepted Answer

Bell-shaped curve

Answer

Skewed distribution

Answer

Uniform distribution

Answer

Bimodal distribution

Question 9

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

Accepted Answer

t-test

Answer

Chi-square test

Answer

ANOVA

Answer

Correlation analysis

Question 10

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

Accepted Answer

Spread

Answer

Mean

Answer

Median

Answer

Mode

Question 11

Which of the following is the best measure of the spread or variability of a dataset?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Range

Question 12

Which of the following is a sampling method in which every member of the population has an equal chance of being selected?

Accepted Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Answer

Quota sampling

Question 13

A researcher wants to estimate the mean height of all students in a school. They randomly select and measure the height of 100 students. What type of sampling is this?

Accepted Answer

Simple random sampling

Answer

Convenience sampling

Answer

Systematic sampling

Answer

Stratified sampling

Question 14

Which scatterplot shows a positive correlation?

Accepted Answer

A plot with points that form a line sloping upwards from left to right

Answer

A plot with points that form a line sloping downwards from left to right

Answer

A plot with points that form a horizontal line

Answer

A plot with points that form a vertical line

Question 15

Which of the following is an unethical practice in statistical analysis?

Accepted Answer

Selling data to third parties without consent

Answer

Protecting participant privacy

Answer

Ensuring data accuracy and transparency

Answer

Using statistical methods responsibly

Question 16

According to the Central Limit Theorem, what distribution do we anticipate for sample means taken from a population?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Uniform distribution

Answer

Logarithmic distribution

Question 17

What is the primary objective of statistical hypothesis testing?

Accepted Answer

To draw conclusions about a population using a sample and determine if there is enough evidence to reject a null hypothesis

Answer

To verify a statement about a population using sample data

Answer

To forecast future events based on historical data

Answer

To condense data using descriptive statistics

Question 18

Which type of data can be measured and counted?

Accepted Answer

Quantitative data

Answer

Qualitative data

Question 19

Which sampling method gives every person in a population an equal chance of being selected?

Accepted Answer

Simple random sampling

Answer

Systematic sampling

Answer

Convenience sampling

Question 20

Which measure of central tendency is most appropriate for a skewed distribution of data?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Standard deviation

Question 21

Which of these is NOT a measure of central tendency?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 22

What is a statistic?

Accepted Answer

A number describing a sample

Answer

A number describing a population

Answer

A collection of data

Answer

A graph of data

Question 23

Which measure of central tendency is calculated by summing all the values and dividing by the number of values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 24

Which of these is a non-parametric statistical test?

Accepted Answer

Mann-Whitney U test

Answer

t-test

Answer

chi-squared test

Answer

ANOVA

Question 25

A researcher wants to determine if there is a relationship between two variables. Which statistical method should they use?

Accepted Answer

Correlation

Answer

Regression

Answer

Hypothesis testing

Answer

Analysis of variance

Question 26

The median of a dataset is the value that occurs:

Accepted Answer

Exactly in the middle

Answer

Most frequently

Answer

Least frequently

Answer

Halfway between the mean and the mode

Question 27

What is the purpose of a statistical hypothesis test?

Accepted Answer

To make a decision about a hypothesis

Answer

To prove a hypothesis

Answer

To collect data

Answer

To disprove a hypothesis

Question 28

Which measure represents the central value of a dataset?

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 29

How is the mean different from the median?

Accepted Answer

The mean can be affected by outliers, whereas the median is not.

Answer

The median is always less than or equal to the mean.

Answer

The mean is always greater than or equal to the median.

Answer

The mean and median are identical in any dataset.

Question 30

What is the probability of rolling an even number on a fair six-sided die?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/6

Question 31

Which of the following is NOT a measure of central tendency: mean, median, or mode?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 32

Which type of graph is most suitable for displaying the distribution of a dataset?

Accepted Answer

Histogram

Answer

Bar chart

Answer

Line chart

Answer

Scatterplot

Question 33

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

Accepted Answer

Spread

Answer

Mean

Answer

Median

Answer

Mode

Question 34

Find the median of the following set of numbers: 5, 7, 3, 9, 6

Accepted Answer

7

Answer

5

Answer

6

Answer

8

Question 35

What is the purpose of a histogram?

Accepted Answer

To display the distribution of a continuous variable.

Answer

To show the relationship between two variables.

Answer

To compare two or more groups.

Answer

To make predictions about future events.

Question 36

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

Accepted Answer

Range

Answer

Median

Answer

Mode

Answer

Mean

Question 37

Which of the following is a graphical representation of data?

Accepted Answer

Histogram

Answer

Table

Answer

Text

Answer

Equation

Question 38

What is an advantage of using a histogram to represent data?

Accepted Answer

It can show the distribution of data.

Answer

It is easy to construct.

Answer

It is aesthetically pleasing.

Answer

It can predict future trends.

Question 39

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

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Correlation coefficient

Question 40

What is the formula for calculating the mean of a set of numbers?

Accepted Answer

Sum of all values divided by the number of values

Answer

Number of values - Smallest value

Answer

Largest value - Smallest value

Answer

Sum of all values

Question 41

What is the formula for calculating the standard deviation of a data set?

Accepted Answer

Square root of the variance

Answer

Sum of all values

Answer

Largest value - Smallest value

Question 42

Which type of probability is based on the known rules of chance?

Accepted Answer

Theoretical

Answer

Empirical

Answer

Subjective

Answer

Experimental

Question 43

What is the probability of rolling an even number on a fair six-sided die?

Accepted Answer

1/2

Answer

1/3

Answer

1/5

Answer

1/4

Question 44

What is the difference between a population and a sample?

Accepted Answer

A population includes all individuals of interest, while a sample is a subset of the population.

Answer

A population is smaller than a sample.

Answer

A sample is always representative of the population.

Question 45

Which sampling method ensures that every member of the population has an equal chance of being selected?

Accepted Answer

Simple random sampling

Answer

Quota sampling

Answer

Stratified sampling

Question 46

What is the main purpose of conducting a hypothesis test?

Accepted Answer

To determine whether there is enough evidence to reject a null hypothesis.

Answer

To collect data about a population.

Answer

To prove that a hypothesis is true.

Question 47

Which of the following is a measure of central tendency?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Range

Question 48

Which of the following is a measure of dispersion?

Accepted Answer

Standard deviation

Answer

Mode

Answer

Mean

Answer

Median

Question 49

Which of the following scatterplots shows a negative correlation?

Accepted Answer

Scatterplot with points forming a downward sloping line

Answer

Scatterplot with points forming an upward sloping line

Answer

Scatterplot with points randomly scattered

Question 50

What is a limitation of using statistics?

Accepted Answer

Data may be biased.

Answer

Statistics are always accurate.

Answer

Statistics can only be used with large data sets.

Answer

Statistics can be used to prove anything.

Question 51

What is the purpose of drawing a histogram?

Accepted Answer

To visualize the distribution of data.

Answer

To find the mean of a data set

Answer

To compare two data sets

Answer

To calculate the standard deviation of a data set

Question 52

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 53

Which of the following is the most appropriate measure of dispersion for a dataset with outliers?

Accepted Answer

Interquartile range

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 54

When representing data graphically, which type of graph is used to show the distribution of data?

Accepted Answer

Histogram

Answer

Bar chart

Answer

Pie chart

Answer

Scatter plot

Question 55

Which of the following is a reasonable application of statistics?

Accepted Answer

Making predictions about a population based on a sample.

Answer

Proving a theory

Answer

Forecasting future events with 100% accuracy