Topic 13 Statistics

Question 1

What is the definition of statistics?

Answer 1

Statistics is the branch of mathematics dealing with data collection, analysis, interpretation, presentation, and organization.

Question 2

True or False: A population includes all members of a specified group.

Answer 2

True

Question 3

What is a sample in statistics?

Answer 3

A sample is a subset of a population used to represent the whole population.

Question 4

What is the difference between descriptive and inferential statistics?

Answer 4

Descriptive statistics summarize and describe the characteristics of a dataset, while inferential statistics use a sample to make predictions or inferences about a population.

Question 5

Fill in the blank: The _____ is the average of a set of numbers.

Answer 5

mean

Question 6

What is the median?

Answer 6

The median is the middle value in a list of numbers ordered from least to greatest.

Question 7

What is the mode?

Answer 7

The mode is the value that appears most frequently in a data set.

Question 8

True or False: The range is the difference between the highest and lowest values in a data set.

Answer 8

True

Question 9

What is a frequency distribution?

Answer 9

A frequency distribution is a summary of how often each different value occurs in a dataset.

Question 10

Define ‘outlier’ in statistics.

Answer 10

An outlier is a data point that differs significantly from other observations in a dataset.

Question 11

What is a histogram?

Answer 11

A histogram is a graphical representation of the distribution of numerical data, using bars to show the frequency of data within certain intervals.

Question 12

What does a box plot display?

Answer 12

A box plot displays the median, quartiles, and potential outliers of a dataset.

Question 13

What is variance?

Answer 13

Variance is a measure of how much values in a dataset differ from the mean.

Question 14

What is standard deviation?

Answer 14

Standard deviation is the square root of the variance and measures the dispersion of a dataset.

Question 15

True or False: A lower standard deviation indicates that data points tend to be close to the mean.

Answer 15

True

Question 16

What is a probability?

Answer 16

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Question 17

Fill in the blank: The _____ of an event is the number of favorable outcomes divided by the total number of possible outcomes.

Answer 17

probability

Question 18

What is a random variable?

Answer 18

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.

Question 19

Define ‘normal distribution’.

Answer 19

Normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence.

Question 20

What is the Central Limit Theorem?

Answer 20

The Central Limit Theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population’s distribution.

Question 21

What is a null hypothesis?

Answer 21

A null hypothesis is a statement that there is no effect or no difference, and it is the hypothesis that researchers aim to test.

Question 22

What is a p-value?

Answer 22

A p-value is the probability of obtaining results at least as extreme as the observed results, assuming that the null hypothesis is true.

Question 23

True or False: A smaller p-value indicates stronger evidence against the null hypothesis.

Answer 23

True

Question 24

What is a confidence interval?

Answer 24

A confidence interval is a range of values derived from a data set that is likely to contain the value of an unknown population parameter.

Question 25

What does '95% confidence interval' mean?

Answer 25

A 95% confidence interval means that if we were to take many samples and build a confidence interval from each sample, approximately 95% of those intervals would contain the true population parameter.

Question 26

Fill in the blank: The _____ is the value that divides a dataset into two equal halves.

Answer 26

median

Question 27

What is skewness?

Answer 27

Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable.

Question 28

What does a positive skew indicate?

Answer 28

A positive skew indicates that the tail on the right side of the distribution is longer or fatter than the left side.

Question 29

What does a negative skew indicate?

Answer 29

A negative skew indicates that the tail on the left side of the distribution is longer or fatter than the right side.

Question 30

Define 'bimodal distribution'.

Answer 30

A bimodal distribution is a distribution with two different modes, or peaks.

Question 31

What is a scatter plot?

Answer 31

A scatter plot is a graph that shows the relationship between two quantitative variables by displaying points for each observation.

Question 32

What is correlation?

Answer 32

Correlation is a statistical measure that describes the strength and direction of a relationship between two variables.

Question 33

True or False: A correlation coefficient of 1 indicates a perfect positive correlation.

Answer 33

True

Question 34

What is the range of the correlation coefficient?

Answer 34

The range of the correlation coefficient is from -1 to 1.

Question 35

What is a regression line?

Answer 35

A regression line is a line that best fits the data points in a scatter plot, used to predict the value of a dependent variable based on the value of an independent variable.

Question 36

What is the purpose of a chi-squared test?

Answer 36

The chi-squared test is used to determine whether there is a significant association between two categorical variables.

Question 37

What does it mean if the chi-squared test results in a significant p-value?

Answer 37

It means that there is enough evidence to reject the null hypothesis of no association between the variables.

Question 38

Fill in the blank: The _____ is the sum of the squared differences between each data point and the mean.

Answer 38

variance

Question 39

What is a simulation in statistics?

Answer 39

A simulation is a method for modeling the behavior of a system or process using random sampling to generate data.

Question 40

What is the purpose of a hypothesis test?

Answer 40

The purpose of a hypothesis test is to determine whether there is enough statistical evidence to support a specific hypothesis about a population parameter.

Question 41

What is the difference between Type I and Type II errors?

Answer 41

Type I error occurs when the null hypothesis is incorrectly rejected, while Type II error occurs when the null hypothesis is not rejected when it is false.

Question 42

What is the significance level in hypothesis testing?

Answer 42

The significance level is the probability of making a Type I error, commonly denoted by alpha (α).

Question 43

True or False: In a two-tailed test, the critical region is split between both tails of the distribution.

Answer 43

True

Question 44

What is a non-parametric test?

Answer 44

A non-parametric test is a statistical test that does not assume a specific distribution for the data.

Question 45

What is the purpose of ANOVA?

Answer 45

ANOVA (Analysis of Variance) is used to compare means among three or more groups to determine if at least one group mean is significantly different from the others.