Two Way Tables | Mathematics for GCSE/IGCSE - Year 11 PDF Download

What are two-way tables?

• Two-way tables help analyze two characteristics within a dataset.
  • For instance, we might look at the number of students studying Spanish or German.
    • We could also consider the number of those students in year 12 versus year 13.
  • One characteristic (e.g., Spanish/German) is shown in columns, the other (e.g., year 12/13) in rows.
• Two-way tables should include row totals and column totals.
  • These totals are also known as marginal or sub-totals.
  • The grand total is where row and column totals intersect.
  • Marginal totals are useful in two-way table questions.
    • If not provided, add marginal totals to the table.
• Completed two-way tables with marginal totals help determine probabilities.

How do I draw and complete a two-way table?

• Once a two-way table is constructed with marginal totals, the enclosed values can aid in calculating probabilities.
  • Identify two characteristics from the question to form rows and columns.
  • Include an additional row and column for marginal totals and the grand total.
  • Gradually fill in the table by extracting information from the question.
• Work your way through each sentence in the question
  • Fill in any values you can directly from the information given.
  • Be prepared to come back to any information that cannot be put into the two-way table directly. Some information may need combining to deduce a value.
    • Some information may need combining in order to deduce a value.

How do I find probabilities from a two-way table?

• When faced with a probability question, it's crucial to translate it into probability phrases. This involves thinking in terms of AND and OR statements.
  • For instance, if you're asked about the likelihood of selecting a year 12 student who studies German, you should rephrase it as P("year 12 AND German").
• Understanding which parts of the two-way table are necessary is key. The numerator comes from the intersection of the row/column for "year 12" and "German".
  • The denominator represents the total of the group being chosen from. This could be a row/column total or the grand total.
  • For example, if you're selecting only year 12 students, the denominator would be the total for the year 12 row/column.

How do I work with two-way tables and conditional probability?

• Conditional probabilities focus on a subset of data in a two-way table.
  • For instance, to find the probability of a male student studying German, consider only the 'male' row or column.
  • Conditional probability questions often use the phrase 'given that...'
• Example: "Find the probability that a randomly chosen student studies German, given that the student is male."
  • The probability is found by dividing the number of 'male AND German' students by the total number of male students.
  • Conditional probabilities are sometimes denoted with 'straight bar' notation: P(A | B).
• This is read as 'the probability of A given B.'
  • Example: P(German | male) represents the probability that a student studies German, given that the student is male.