Data Analysis for Year 12 Mathematics: Interactive Quizzes and Practice

Question 1

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

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 2

The range of a set of numbers is the difference between the highest and lowest numbers in the set.

Accepted Answer

True

Answer

False

Question 3

The standard deviation is a measure of how spread out a set of numbers is. What is the appropriate unit of measurement for standard deviation?

Accepted Answer

Square root of original unit of measurement

Answer

Original unit of measurement

Answer

Square of original unit of measurement

Question 4

A scatterplot can be used to show the relationship between two sets of data. True or False?

Accepted Answer

True

Answer

False

Question 5

In the context of data handling, what does the term 'distribution' refer to?

Accepted Answer

The way in which data is represented

Answer

The way in which data is collected

Answer

The way in which data is organized

Answer

The way in which data is analyzed

Question 6

Which of the following is a measure of central tendency, describing the typical value of a data set?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Range

Answer

Variance

Question 7

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

Accepted Answer

Sum of values / Number of values

Answer

Sum of values / (Number of values - 1)

Answer

Average value - Standard deviation

Answer

Median + Mode / 2

Question 8

Which measure of dispersion indicates the average distance of data points from the mean within a data set?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Range

Question 9

What is the formula for calculating the range of a data set?

Accepted Answer

Maximum value - Minimum value

Answer

Mean - Mode

Answer

Standard deviation / Mean

Answer

Sum of values / Number of values

Question 10

Which of the following is a type of cumulative frequency graph that displays the running total of frequencies?

Accepted Answer

Ogive

Answer

Scatter plot

Answer

Bar chart

Answer

Pie chart

Question 11

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

Accepted Answer

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

Answer

A population is always larger than a sample

Answer

A sample must be representative of the population it is drawn from

Answer

There is no difference between a population and a sample

Question 12

What is the fundamental purpose of conducting a hypothesis test?

Accepted Answer

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

Answer

To predict the outcome of a future event with certainty

Answer

To provide a detailed description of the characteristics of a population

Answer

To collect data and information about a population

Question 13

Which type of graph is best suited for displaying frequency distributions?

Accepted Answer

Histogram

Answer

Bar chart

Answer

Pie chart

Answer

Scatter plot

Question 14

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

Accepted Answer

1/6

Answer

1/2

Answer

1/3

Answer

1/4

Question 15

Which of the following is an example of a categorical variable?

Accepted Answer

Eye colour

Answer

Age

Answer

Height

Answer

Income

Question 16

What is the purpose of a confidence interval?

Accepted Answer

To estimate the true value of a population parameter

Answer

To test a statistical hypothesis

Answer

To predict future outcomes

Answer

To summarize data

Question 17

Which of the following is a non-parametric statistical test?

Accepted Answer

Wilcoxon rank-sum test

Answer

Pearson's chi-squared test

Answer

Student's t-test

Answer

Analysis of variance

Question 18

In a statistical test, what is the null hypothesis?

Accepted Answer

The hypothesis that is assumed to be true

Answer

The hypothesis that is being tested

Answer

The hypothesis that is rejected if the test is significant

Answer

The hypothesis that is accepted if the test is not significant

Question 19

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

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Mode

Question 20

The mean of a set of data is the:

Accepted Answer

Sum of all values divided by the number of values

Answer

Middle value of the data when arranged in ascending order

Answer

Most frequently occurring value

Answer

Value that occurs least frequently

Question 21

Which of the following is a measure of dispersion?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 22

The correlation coefficient (r) measures the:

Accepted Answer

Strength and direction of a linear relationship

Answer

Mean of a set of data

Answer

Range of a set of data

Answer

Mode of a set of data

Question 23

Which of the following is NOT an assumption of the Pearson product-moment correlation coefficient?

Accepted Answer

Bivariate normality

Answer

Linearity

Answer

Homoscedasticity

Answer

Independence of observations

Question 24

Which of the following is a statistical test used to determine if there is a significant difference between the means of two independent groups?

Accepted Answer

t-test

Answer

Chi-square test

Answer

ANOVA

Answer

Regression analysis

Question 25

Which of the following is a statistical test used to determine if there is a significant relationship between two categorical variables?

Accepted Answer

Chi-square test

Answer

t-test

Answer

ANOVA

Answer

Regression analysis

Question 26

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 27

Which of the following is NOT a measure of dispersion?

Accepted Answer

Median

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 28

A data set has a range of 10 and a standard deviation of 4. Which measure of dispersion is more reliable?

Accepted Answer

Standard deviation

Answer

Range

Question 29

In a scatter plot, what indicates a positive correlation between two variables?

Accepted Answer

Points form an upward sloping line

Answer

Points form a downward sloping line

Answer

Points form a horizontal line

Answer

Points form a vertical line

Question 30

In a data set, what indicates the presence of an outlier?

Accepted Answer

A value that is significantly higher or lower than the rest of the data

Answer

A value that is close to the mean

Answer

A value that is in the middle of the data range

Answer

A value that is at the ends of the data range

Question 31

A survey asks participants to rate their satisfaction with a product using a scale of 1 to 5. What type of data is this?

Accepted Answer

Ordinal

Answer

Numerical

Answer

Categorical

Answer

Nominal

Question 32

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

Accepted Answer

Literature review

Answer

Questionnaires

Answer

Interviews

Answer

Observations

Question 33

What is the key difference between the mean and the median?

Accepted Answer

The mean is affected by outliers, while the median is not.

Answer

The median is affected by outliers, while the mean is not.

Answer

The mean is always greater than the median.

Answer

The median is always greater than the mean.

Question 34

Differentiate between a Type I error and a Type II error.

Accepted Answer

A Type I error occurs when the null hypothesis is rejected despite being true, while a Type II error occurs when the null hypothesis is accepted despite being false.

Answer

A Type II error occurs when the null hypothesis is rejected despite being true, while a Type I error occurs when the null hypothesis is accepted despite being false.

Answer

A Type I error is always more severe than a Type II error.

Answer

A Type II error is always more severe than a Type I error.

Question 35

In statistics, how are non-parametric tests used to analyze ordinal or categorical data? Provide specific examples of non-parametric tests and their applications.

Accepted Answer

The Mann-Whitney U test and the Kruskal-Wallis test are non-parametric tests used to compare two or more independent groups with ordinal data.

Accepted Answer

The chi-square test of independence is a non-parametric test used to determine associations between categorical variables.

Answer

Non-parametric tests are exclusively applicable to numerical data.

Answer

Non-parametric tests are inherently superior to parametric tests.

Question 36

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

Accepted Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Answer

Quota sampling

Question 37

What is a key feature of a bimodal or multimodal distribution?

Accepted Answer

Two or more distinct peaks

Answer

A single peak

Answer

A normal bell-shaped curve

Question 38

Which of the following is the most accurate formula for calculating the mean?

Accepted Answer

Sum of all values divided by the number of values

Answer

Median of all values divided by the number of values

Answer

Mode of all values divided by the number of values

Question 39

Which measure of dispersion describes the typical distance of data points from the mean?

Accepted Answer

Standard deviation

Answer

Variance

Answer

Range

Answer

Interquartile range

Question 40

What is the primary purpose of a frequency distribution table?

Accepted Answer

To organize data points based on their frequency of occurrence

Answer

To visually depict data

Answer

To compute the mean of a data set

Question 41

Identify a potential source of bias in data collection

Accepted Answer

Non-representative sample selection

Answer

Utilization of precise measuring instruments

Answer

Consideration of ethical implications

Answer

Clearly defined research question

Question 42

Explain the fundamental difference between qualitative and quantitative data

Accepted Answer

Qualitative data lacks numerical values, while quantitative data contains numerical values

Answer

Qualitative data offers greater reliability compared to quantitative data

Answer

Qualitative data can be collected more easily than quantitative data

Question 43

In a symmetrical distribution, what is the relationship between the mean, median, and mode?

Accepted Answer

They coincide with each other

Answer

Mean < Median < Mode

Answer

Mean > Median > Mode

Answer

Mode > Median > Mean

Question 44

Which of the following is NOT a measure of central tendency that summarizes the middle or center of a data set?

Accepted Answer

Interquartile range

Answer

Mean

Answer

Median

Answer

Mode

Question 45

Which of the following graphs is most appropriate for representing a data set that shows changes over time?

Accepted Answer

Line graph

Answer

Bar chart

Answer

Histogram

Answer

Pie chart

Question 46

Which of the following sampling techniques is most likely to introduce bias into the sample?

Accepted Answer

Convenience sampling

Answer

Stratified sampling

Answer

Systematic sampling

Answer

Random sampling

Question 47

A data set has a skewed distribution. Which of the following measures of central tendency would be most appropriate for this data set?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 48

A box plot is used to represent a data set. The difference between the third quartile and the first quartile is known as the:

Accepted Answer

Interquartile range

Answer

Variance

Answer

Range

Answer

Median

Question 49

Which of these is NOT a measure of central tendency?

Accepted Answer

Range

Answer

Median

Answer

Mode

Answer

Mean

Question 50

What is the range of the data set: 10, 12, 14, 16, 18?

Accepted Answer

8

Answer

14

Answer

10

Answer

12

Question 51

Which graph is most suitable for showing the distribution of exam scores?

Accepted Answer

Histogram

Answer

Pie chart

Answer

Bar chart

Answer

Scatter plot

Question 52

What is the interquartile range (IQR) of the data set: 5, 7, 9, 11, 13, 15, 17?

Accepted Answer

6

Answer

4

Answer

10

Answer

8

Question 53

Which of these is an example of a discrete variable?

Accepted Answer

Number of siblings

Answer

Weight

Answer

Height

Answer

Temperature

Question 54

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

Accepted Answer

1/6

Answer

1/3

Answer

1/5

Answer

1/4

Question 55

Which of these is NOT a typical step in the data handling process?

Accepted Answer

Hypothesis testing

Answer

Data representation

Answer

Data collection

Answer

Data analysis

Question 56

What is the median of the data set: 3, 5, 7, 9, 11, 13?

Accepted Answer

9

Answer

6

Answer

10

Answer

12

Question 57

What is the main purpose of a stem-and-leaf plot?

Accepted Answer

To show the distribution of a data set.

Answer

To calculate the mean of a data set.

Answer

To find the mode of a data set.

Answer

To represent categorical data.