STAT C1000 Statistics Contingency Table Vocabulary

Vocabulary and probability calculations based on the STAT C1000 student enrollment contingency table.

Contingency Table

A type of table in a matrix format that displays the frequency distribution of variables, such as the breakdown of $1600$ students by academic major and class year.

P(Liberal Arts)

The probability of selecting a Liberal Arts major from the total population, calculated as $\frac{668}{1600} = 0.4175$.

P(Sciences and Sophomore)

The joint probability of a student being both a Science major and a Sophomore, calculated as $\frac{42}{1600} = 0.02625$.

P(Sciences or Sophomore)

The probability of selecting a student who is either a Science major or a Sophomore, calculated using the addition rule: $\frac{167 + 417 - 42}{1600} = \frac{542}{1600} = 0.33875$.

P(Junior and Liberal Arts)

The joint probability of a student being both a Junior and a Liberal Arts major, calculated as $\frac{80}{1600} = 0.05$.

P(Liberal Arts or Junior)

The probability of selecting a student who is either a Liberal Arts major or a Junior, calculated as $\frac{668 + 200 - 80}{1600} = \frac{788}{1600} = 0.4925$.

P(Junior, given Liberal Arts)

The conditional probability that a student is a Junior given they are a Liberal Arts major, calculated as $\frac{80}{668} \approx 0.1198$.

P(Sciences, given Freshman)

The conditional probability that a student is a Sciences major given they are a Freshman, calculated as $\frac{92}{850} \approx 0.1082$.

P(Freshman, given Sciences)

The conditional probability that a student is a Freshman given they are a Sciences major, calculated as $\frac{92}{167} \approx 0.5510$.