Grade 8 · Statistics & probability

Two-way tables practice

Two-way tables is a grade 8 math skill aligned to Common Core standard 8.SP.A.4: understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 15 two-way tables problems our math games drill.

CCSS 8.SP.A.415 questions in the bank
Sample questions

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Question 1easy

A two-way table has rows Dog/Cat and columns Boys/Girls: Dog&Boys=10, Dog&Girls=6, Cat&Boys=5, Cat&Girls=9. How many were surveyed in total?

Add all cells: 10+6+5+9=3010+6+5+9=30.

Question 2easy

A two-way table has rows Dog/Cat and columns Boys/Girls: Dog&Boys=10, Dog&Girls=6, Cat&Boys=5, Cat&Girls=9. How many chose Dog in total?

Row total for Dog: 10+6=1610+6=16.

Question 3easy

A two-way table has rows Dog/Cat and columns Boys/Girls: Dog&Boys=10, Dog&Girls=6, Cat&Boys=5, Cat&Girls=9. What fraction of all surveyed were Dog and Boys? Simplify.

1030=13\dfrac{10}{30} = \dfrac{1}{3}.

Question 4easy

A two-way table has rows Bus/Walk and columns 6th/7th: Bus&6th=12, Bus&7th=8, Walk&6th=4, Walk&7th=16. How many were surveyed in total?

Add all cells: 12+8+4+16=4012+8+4+16=40.

Question 5easy

A two-way table has rows Bus/Walk and columns 6th/7th: Bus&6th=12, Bus&7th=8, Walk&6th=4, Walk&7th=16. How many chose Bus in total?

Row total for Bus: 12+8=2012+8=20.

Question 6easy

A two-way table has rows Bus/Walk and columns 6th/7th: Bus&6th=12, Bus&7th=8, Walk&6th=4, Walk&7th=16. What fraction of all surveyed were Bus and 6th? Simplify.

1240=310\dfrac{12}{40} = \dfrac{3}{10}.

Question 7easy

A two-way table has rows Chess/Art and columns 7th/8th: Chess&7th=9, Art&7th=4, Art&8th=11. The Chess row total is 15. How many students are Chess&8th?

Chess row total minus the known Chess cell: 15−9=615-9=6.

Question 8easy

A two-way table has rows Bike/Scooter and columns Morning/Afternoon: Bike&Morning=11, Bike&Afternoon=7, Scooter&Morning=5. In all, 29 trips were recorded. How many trips are Scooter&Afternoon?

The three known cells sum to 11+7+5=2311+7+5=23, so the missing cell is 29−23=629-23=6.

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