Two-way tables: joint, marginal and conditional proportions

About this lesson

Integrated Math I › Descriptive statistics: two variables

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Two-way tables: joint, marginal and conditional proportions

Warm-up

Three quick questions from earlier lessons.

Discover

In a class, 12 of 20 girls and 9 of 15 boys play a sport. Who is more likely to play, a girl or a boy?

  1. Equally likely: 60% each
  2. A girl: 12 is more than 9

Key idea

A two-way table counts cases by two categorical variables.

Joint proportion: a cell ÷ grand total. Marginal proportion: a row or column total ÷ grand total. Conditional proportion: a cell ÷ its row (or column) total: the proportion within one group.

Worked example

Pets: 30 cat owners (18 adults, 12 children), 50 dog owners (35 adults, 15 children).

Joint: adults with cats =1880= \tfrac{18}{80}
Cell ÷ 80.
Marginal: adults =5380= \tfrac{53}{80}
Column total ÷ 80.
Conditional: adults among cat owners =1830=0.6= \tfrac{18}{30} = 0.6
Within cat owners.

Your turn, guided

Your turn: children among dog owners.

0.30.3
15 of 50.

Practice ★

  1. A survey asked 145 people whether they exercise weekly. Under 30: 22 yes, 43 no. Age 30 or over: 27 yes, 53 no. What proportion of the under-30s exercise weekly?
  2. A survey asked 121 people whether they exercise weekly. Under 30: 59 yes, 12 no. Age 30 or over: 23 yes, 27 no. What proportion of the under-30s exercise weekly?
  3. A survey asked 150 people whether they exercise weekly. Under 30: 41 yes, 40 no. Age 30 or over: 19 yes, 50 no. What proportion of the under-30s exercise weekly?

Watch out!

Practice ★★

  1. A survey asked 124 people whether they exercise weekly. Under 30: 21 yes, 50 no. Age 30 or over: 31 yes, 22 no. What proportion of all the people exercise weekly?
  1. A survey asked 140 people whether they exercise weekly. Under 30: 47 yes, 17 no. Age 30 or over: 37 yes, 39 no. What proportion of all the people are under 30 and exercise weekly?
  2. A survey asked 135 people whether they exercise weekly. Under 30: 44 yes, 25 no. Age 30 or over: 10 yes, 56 no. What proportion of all the people are under 30 and exercise weekly?

Exit ticket

Three questions to check you have got it.

  1. A survey asked 145 people whether they exercise weekly. Under 30: 22 yes, 43 no. Age 30 or over: 27 yes, 53 no. What proportion of the under-30s exercise weekly?
  2. A survey asked 121 people whether they exercise weekly. Under 30: 59 yes, 12 no. Age 30 or over: 23 yes, 27 no. What proportion of the under-30s exercise weekly?
  3. A survey asked 150 people whether they exercise weekly. Under 30: 41 yes, 40 no. Age 30 or over: 19 yes, 50 no. What proportion of the under-30s exercise weekly?

Summary card

Two-way tables

  • Joint: cell / total. Marginal: margin / total.
  • Conditional: cell / its group total.

Watch out: name the group you condition on.

End of the lesson

Next lesson: Association between categorical variables Back to the chapter

Answers: Two-way tables: joint, marginal and conditional proportions

A

  1. 2265\frac{22}{65}
  2. 5971\frac{59}{71}
  3. 4181\frac{41}{81}

B

  1. 1331\frac{13}{31}

C

  1. 47140\frac{47}{140}
  2. 44135\frac{44}{135}

D

  1. 2265\frac{22}{65}
  2. 5971\frac{59}{71}
  3. 4181\frac{41}{81}

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