Exploring Two-way Tables and Probability

What is a two-way table used for?

• To perform regression analysis

• To graphically represent data

• To calculate the mean of a dataset

• To display the frequencies of two categories

What does the term 'marginal frequency' refer to?

• The frequency of the most common category

• The average frequency of all categories

• The total frequency of one category

• The frequency of the least common category

What is the purpose of calculating the grand total in a two-way table?

• To determine the range of the data

• To identify the most frequent category

• To calculate the mean value of the data

• To find the total number of observations

In the context of a two-way table, what does 'total attending' represent?

• The sum of all students attending an event

• The average number of students attending

• The difference between attendees and non-attendees

• The ratio of attendees to the total surveyed

How is a joint relative frequency calculated?

• By dividing the joint frequency by the grand total

• By multiplying the joint frequencies of two categories

• By adding the marginal frequencies of two categories

• By subtracting the marginal frequency from the grand total

How do you find a marginal relative frequency?

• By subtracting the joint frequency from the marginal frequency

• By summing the joint relative frequencies in a row or column

• By multiplying the joint frequencies by the grand total

• By dividing the marginal frequency by the number of categories

What does a conditional relative frequency provide?

• The ratio of a joint frequency to its row or column total

• The total number of observations in a study

• The sum of all joint frequencies in a table

• The difference between two marginal frequencies

What is the significance of the 'conditional' in conditional relative frequencies?

• It implies the frequency is only conditionally accepted as accurate

• It indicates the frequency is based on a specific condition or subset

• It means the frequency is conditioned to change over time

• It signifies that the frequency is conditional upon external factors

How can you determine if two events are independent based on conditional probabilities?

• If one event's probability is twice the other's

• If the sum of the probabilities equals 1

• If the probabilities of the events are equal

• If the probabilities of the events are opposites

Which route should the jogger choose based on conditional probabilities?

• Route B, as it has the highest success rate

• Route A, as it is the least crowded

• Route A, due to its shorter distance

• Route C, because it is the most scenic