Is there an association? Compare each row's; percent in the Electric column.; Electric Gas Total; Cars 10 15 25; Trucks 20 5 25; Total 30 20 50;

Yes: 40% of Cars and 80% of Trucks

Is there an association? Compare each row's; percent in the Indoor column.; Indoor Outdoor Total; Cats 20 20 40; Dogs 15 5 20; Total 35 25 60;

Yes: 50% of Cats and 75% of Dogs

Are the events “Drive” and “Seniors” independent?; Round each probability to the nearest hundredth before you compare.; Drive Bus; Juniors 18 12; Seniors 12 8;

Yes: P(Drive Seniors) = 0.60 = P(Drive)

Are the events “Coffee” and “Teens” independent?; Round each probability to the nearest hundredth before you compare.; Coffee Tea; Adults 4 16; Teens 9 16;

No: P(Coffee Teens) = 0.36, but P(Coffee) = 0.29

A middle school surveyed 95 sixth and seventh graders about pets. 29 students do not have a pet. Of these, 2 are seventh graders. Also, 11 sixth graders have one. Complete the two-way table.; Pet No pet Total; Sixth graders 1.2em 1.2em 1.2em; Seventh graders 1.2em 1.2em 1.2em; Total 1.2em 1.2em 1.2em;

Sixth graders: 11 have a pet, 27 do not, 38 in all. Seventh graders: 55 have a pet, 2 do not, 57 in all. Totals: 66 have a pet, 29 do not, 95 in all.

A music teacher surveyed 85 juniors and seniors about whether they play an instrument. Of the juniors, 40 play one and 15 do not play one. In all, 41 do not play an instrument. Complete the two-way table.; Instrument None Total; Juniors 1.2em 1.2em 1.2em; Seniors 1.2em 1.2em 1.2em; Total 1.2em 1.2em 1.2em;

Juniors: 40 play an instrument, 15 do not, 55 in all. Seniors: 4 play an instrument, 26 do not, 30 in all. Totals: 44 play an instrument, 41 do not, 85 in all.

Is there an association? Compare each row's; percent in the Indoor column.; Indoor Outdoor Total; Cats 8 32 40; Dogs 32 8 40; Total 40 40 80;

Yes: 20% of Cats and 80% of Dogs

Are the events “Drive” and “Seniors” independent?; Round each probability to the nearest hundredth before you compare.; Drive Bus; Juniors 20 30; Seniors 12 8;

No: P(Drive Seniors) = 0.60, but P(Drive) = 0.46

70 sixth and seventh graders were asked whether they have a pet. 33 sixth graders have a pet, and 4 sixth graders do not have one. Of the seventh graders, 23 have one. Complete the two-way table.; Pet No pet Total; Sixth graders 1.2em 1.2em 1.2em; Seventh graders 1.2em 1.2em 1.2em; Total 1.2em 1.2em 1.2em;

Sixth graders: 33 have a pet, 4 do not, 37 in all. Seventh graders: 23 have a pet, 10 do not, 33 in all. Totals: 56 have a pet, 14 do not, 70 in all.

Worksheets · Statistics

Two-way frequency tables worksheet for Statistics

A two-way table counts two things at once. Every row and column adds to its total, which is how a missing cell is found. A relative frequency divides a cell by the grand total; a conditional one divides by the total of just the row or column it sits in.

Also taught in Algebra 2, Pre-Algebra and Algebra 1, each at its own level and with its own examples.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Two-Way Tables Date Period Use each table. Fill in the missing value $\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 3 & __ & 15 \\ Trucks & 20 & 20 & 40 \\ Total & 23 & 32 & 55 \end{array} \end{aligned}$ $\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & __ & 12 & 30 \\ Sophomores & 19 & 15 & 34 \\ Total & 37 & 27 & 64 \end{array} \end{aligned}$ $\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 14 & __ & 29 \\ Weekend shoppers & 7 & 9 & 16 \\ Total & 21 & 24 & 45 \end{array} \end{aligned}$ Find a fraction of the whole table $\begin{aligned} What fraction of the vehicles are Cars and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 30 & 19 & 49 \\ Trucks & 40 & 20 & 60 \\ Total & 70 & 39 & 109 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the pets are Dogs and 5 and over? \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 39 & 8 & 47 \\ Cats & 40 & 9 & 49 \\ Total & 79 & 17 & 96 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the students are Freshmen and No phone? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 13 & 38 & 51 \\ Sophomores & 39 & 9 & 48 \\ Total & 52 & 47 & 99 \end{array} \end{aligned}$ Find a percent of the whole table $\begin{aligned} What percent of the students are Boys and Athletes? \\ \begin{array}{lcc} Athletes & Non-athletes \\ Boys & 7 & 8 \\ Girls & 2 & 3 \end{array} \end{aligned}$ $\begin{aligned} What percent of the students are Boys and Non-athletes? \\ \begin{array}{lcc} Athletes & Non-athletes \\ Boys & 5 & 34 \\ Girls & 8 & 3 \end{array} \end{aligned}$ Find a conditional relative frequency $\begin{aligned} What fraction of the Girls are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 10 & 13 & 23 \\ Girls & 17 & 8 & 25 \\ Total & 27 & 21 & 48 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the Athletes are Girls? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 8 & 19 & 27 \\ Girls & 8 & 5 & 13 \\ Total & 16 & 24 & 40 \end{array} \end{aligned}$ Find a marginal percent $\begin{aligned} What percent of the adults are in the Coffee column? \\ Round to the nearest percent. \\ \begin{array}{lccc} Coffee & Tea & Total \\ Under 30 & 10 & 30 & 40 \\ 30 and over & 20 & 32 & 52 \\ Total & 30 & 62 & 92 \end{array} \end{aligned}$ $\begin{aligned} What percent of the vehicles are in the Electric column? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 8 & 5 & 13 \\ Trucks & 14 & 28 & 42 \\ Total & 22 & 33 & 55 \end{array} \end{aligned}$ Decide if there is an association $\begin{aligned} Is there an association? Compare each row’s \\ percent in the Electric column. \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 10 & 15 & 25 \\ Trucks & 20 & 5 & 25 \\ Total & 30 & 20 & 50 \end{array} \end{aligned}$ $\begin{aligned} Is there an association? Compare each row’s \\ percent in the Indoor column. \\ \begin{array}{lccc} Indoor & Outdoor & Total \\ Cats & 20 & 20 & 40 \\ Dogs & 15 & 5 & 20 \\ Total & 35 & 25 & 60 \end{array} \end{aligned}$ Decide if the events are independent $\begin{aligned} Are the events “Drive” and “Seniors” independent? \\ Round each probability to the nearest hundredth before you compare. \\ \begin{array}{lcc} Drive & Bus \\ Juniors & 18 & 12 \\ Seniors & 12 & 8 \end{array} \end{aligned}$ $\begin{aligned} Are the events “Coffee” and “Teens” independent? \\ Round each probability to the nearest hundredth before you compare. \\ \begin{array}{lcc} Coffee & Tea \\ Adults & 4 & 16 \\ Teens & 9 & 16 \end{array} \end{aligned}$ Build the two-way table from a description $\begin{aligned} A middle school surveyed 95 sixth and seventh graders about pets. 29 students do not have a pet. Of these, 2 are seventh graders. Also, 11 sixth graders have one. Complete the two-way table. \\ \begin{array}{lccc} Pet & No pet & Total \\ Sixth graders \\ Seventh graders \\ Total \end{array} \end{aligned}$ $\begin{aligned} A music teacher surveyed 85 juniors and seniors about whether they play an instrument. Of the juniors, 40 play one and 15 do not play one. In all, 41 do not play an instrument. Complete the two-way table. \\ \begin{array}{lccc} Instrument & None & Total \\ Juniors \\ Seniors \\ Total \end{array} \end{aligned}$ Find a conditional percent $\begin{aligned} What percent of the cars are hybrid? Round to the nearest tenth. \\ \begin{array}{lccc} Electric & Gas & Hybrid \\ Car & 39 & 38 & 29 \\ Truck & 37 & 34 & 38 \end{array} \end{aligned}$ $\begin{aligned} What percent of the hybrid vehicles are cars? Round to the nearest tenth. \\ \begin{array}{lccc} Electric & Gas & Hybrid \\ Car & 11 & 6 & 8 \\ Truck & 18 & 23 & 13 \end{array} \end{aligned}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Two-Way Tables

Date Period

Use each table.

Fill in the missing value
$\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 3 & __ & 15 \\ Trucks & 20 & 20 & 40 \\ Total & 23 & 32 & 55 \end{array} \end{aligned}$
$\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & __ & 12 & 30 \\ Sophomores & 19 & 15 & 34 \\ Total & 37 & 27 & 64 \end{array} \end{aligned}$
$\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 14 & __ & 29 \\ Weekend shoppers & 7 & 9 & 16 \\ Total & 21 & 24 & 45 \end{array} \end{aligned}$

Find a fraction of the whole table
$\begin{aligned} What fraction of the vehicles are Cars and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 30 & 19 & 49 \\ Trucks & 40 & 20 & 60 \\ Total & 70 & 39 & 109 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the pets are Dogs and 5 and over? \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 39 & 8 & 47 \\ Cats & 40 & 9 & 49 \\ Total & 79 & 17 & 96 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the students are Freshmen and No phone? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 13 & 38 & 51 \\ Sophomores & 39 & 9 & 48 \\ Total & 52 & 47 & 99 \end{array} \end{aligned}$

Find a percent of the whole table
$\begin{aligned} What percent of the students are Boys and Athletes? \\ \begin{array}{lcc} Athletes & Non-athletes \\ Boys & 7 & 8 \\ Girls & 2 & 3 \end{array} \end{aligned}$
$\begin{aligned} What percent of the students are Boys and Non-athletes? \\ \begin{array}{lcc} Athletes & Non-athletes \\ Boys & 5 & 34 \\ Girls & 8 & 3 \end{array} \end{aligned}$

Find a conditional relative frequency
$\begin{aligned} What fraction of the Girls are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 10 & 13 & 23 \\ Girls & 17 & 8 & 25 \\ Total & 27 & 21 & 48 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the Athletes are Girls? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 8 & 19 & 27 \\ Girls & 8 & 5 & 13 \\ Total & 16 & 24 & 40 \end{array} \end{aligned}$

Find a marginal percent
$\begin{aligned} What percent of the adults are in the Coffee column? \\ Round to the nearest percent. \\ \begin{array}{lccc} Coffee & Tea & Total \\ Under 30 & 10 & 30 & 40 \\ 30 and over & 20 & 32 & 52 \\ Total & 30 & 62 & 92 \end{array} \end{aligned}$
$\begin{aligned} What percent of the vehicles are in the Electric column? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 8 & 5 & 13 \\ Trucks & 14 & 28 & 42 \\ Total & 22 & 33 & 55 \end{array} \end{aligned}$

Decide if there is an association
$\begin{aligned} Is there an association? Compare each row’s \\ percent in the Electric column. \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 10 & 15 & 25 \\ Trucks & 20 & 5 & 25 \\ Total & 30 & 20 & 50 \end{array} \end{aligned}$
$\begin{aligned} Is there an association? Compare each row’s \\ percent in the Indoor column. \\ \begin{array}{lccc} Indoor & Outdoor & Total \\ Cats & 20 & 20 & 40 \\ Dogs & 15 & 5 & 20 \\ Total & 35 & 25 & 60 \end{array} \end{aligned}$

Decide if the events are independent
$\begin{aligned} Are the events “Drive” and “Seniors” independent? \\ Round each probability to the nearest hundredth before you compare. \\ \begin{array}{lcc} Drive & Bus \\ Juniors & 18 & 12 \\ Seniors & 12 & 8 \end{array} \end{aligned}$
$\begin{aligned} Are the events “Coffee” and “Teens” independent? \\ Round each probability to the nearest hundredth before you compare. \\ \begin{array}{lcc} Coffee & Tea \\ Adults & 4 & 16 \\ Teens & 9 & 16 \end{array} \end{aligned}$

Build the two-way table from a description
$\begin{aligned} A middle school surveyed 95 sixth and seventh graders about pets. 29 students do not have a pet. Of these, 2 are seventh graders. Also, 11 sixth graders have one. Complete the two-way table. \\ \begin{array}{lccc} Pet & No pet & Total \\ Sixth graders \\ Seventh graders \\ Total \end{array} \end{aligned}$
$\begin{aligned} A music teacher surveyed 85 juniors and seniors about whether they play an instrument. Of the juniors, 40 play one and 15 do not play one. In all, 41 do not play an instrument. Complete the two-way table. \\ \begin{array}{lccc} Instrument & None & Total \\ Juniors \\ Seniors \\ Total \end{array} \end{aligned}$

Find a conditional percent
$\begin{aligned} What percent of the cars are hybrid? Round to the nearest tenth. \\ \begin{array}{lccc} Electric & Gas & Hybrid \\ Car & 39 & 38 & 29 \\ Truck & 37 & 34 & 38 \end{array} \end{aligned}$
$\begin{aligned} What percent of the hybrid vehicles are cars? Round to the nearest tenth. \\ \begin{array}{lccc} Electric & Gas & Hybrid \\ Car & 11 & 6 & 8 \\ Truck & 18 & 23 & 13 \end{array} \end{aligned}$



Sigma Prep · sigmaprep.io/worksheets Name Two-Way TablesAnswer keyVersion 1 Date Period Use each table. Fill in the missing value $\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 3 & __ & 15 \\ Trucks & 20 & 20 & 40 \\ Total & 23 & 32 & 55 \end{array} \end{aligned}$ $12$ $\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & __ & 12 & 30 \\ Sophomores & 19 & 15 & 34 \\ Total & 37 & 27 & 64 \end{array} \end{aligned}$ $18$ $\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 14 & __ & 29 \\ Weekend shoppers & 7 & 9 & 16 \\ Total & 21 & 24 & 45 \end{array} \end{aligned}$ $15$ Find a fraction of the whole table $\begin{aligned} What fraction of the vehicles are Cars and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 30 & 19 & 49 \\ Trucks & 40 & 20 & 60 \\ Total & 70 & 39 & 109 \end{array} \end{aligned}$ $\frac{19}{109}$ $\begin{aligned} What fraction of the pets are Dogs and 5 and over? \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 39 & 8 & 47 \\ Cats & 40 & 9 & 49 \\ Total & 79 & 17 & 96 \end{array} \end{aligned}$ $\frac{1}{12}$ $\begin{aligned} What fraction of the students are Freshmen and No phone? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 13 & 38 & 51 \\ Sophomores & 39 & 9 & 48 \\ Total & 52 & 47 & 99 \end{array} \end{aligned}$ $\frac{38}{99}$ Find a percent of the whole table $\begin{aligned} What percent of the students are Boys and Athletes? \\ \begin{array}{lcc} Athletes & Non-athletes \\ Boys & 7 & 8 \\ Girls & 2 & 3 \end{array} \end{aligned}$ $35 %$ $\begin{aligned} What percent of the students are Boys and Non-athletes? \\ \begin{array}{lcc} Athletes & Non-athletes \\ Boys & 5 & 34 \\ Girls & 8 & 3 \end{array} \end{aligned}$ $68 %$ Find a conditional relative frequency $\begin{aligned} What fraction of the Girls are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 10 & 13 & 23 \\ Girls & 17 & 8 & 25 \\ Total & 27 & 21 & 48 \end{array} \end{aligned}$ $\frac{8}{25}$ $\begin{aligned} What fraction of the Athletes are Girls? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 8 & 19 & 27 \\ Girls & 8 & 5 & 13 \\ Total & 16 & 24 & 40 \end{array} \end{aligned}$ $\frac{1}{2}$ Find a marginal percent $\begin{aligned} What percent of the adults are in the Coffee column? \\ Round to the nearest percent. \\ \begin{array}{lccc} Coffee & Tea & Total \\ Under 30 & 10 & 30 & 40 \\ 30 and over & 20 & 32 & 52 \\ Total & 30 & 62 & 92 \end{array} \end{aligned}$ $33 %$ $\begin{aligned} What percent of the vehicles are in the Electric column? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 8 & 5 & 13 \\ Trucks & 14 & 28 & 42 \\ Total & 22 & 33 & 55 \end{array} \end{aligned}$ $40 %$ Decide if there is an association $\begin{aligned} Is there an association? Compare each row’s \\ percent in the Electric column. \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 10 & 15 & 25 \\ Trucks & 20 & 5 & 25 \\ Total & 30 & 20 & 50 \end{array} \end{aligned}$ Yes: $40 %$ of Cars and $80 %$ of Trucks $\begin{aligned} Is there an association? Compare each row’s \\ percent in the Indoor column. \\ \begin{array}{lccc} Indoor & Outdoor & Total \\ Cats & 20 & 20 & 40 \\ Dogs & 15 & 5 & 20 \\ Total & 35 & 25 & 60 \end{array} \end{aligned}$ Yes: $50 %$ of Cats and $75 %$ of Dogs Decide if the events are independent $\begin{aligned} Are the events “Drive” and “Seniors” independent? \\ Round each probability to the nearest hundredth before you compare. \\ \begin{array}{lcc} Drive & Bus \\ Juniors & 18 & 12 \\ Seniors & 12 & 8 \end{array} \end{aligned}$ Yes: $P ($ Drive $∣$ Seniors $) = 0.60 = P ($ Drive $)$ $\begin{aligned} Are the events “Coffee” and “Teens” independent? \\ Round each probability to the nearest hundredth before you compare. \\ \begin{array}{lcc} Coffee & Tea \\ Adults & 4 & 16 \\ Teens & 9 & 16 \end{array} \end{aligned}$ No: $P ($ Coffee $∣$ Teens $) = 0.36$ , but $P ($ Coffee $) = 0.29$ Build the two-way table from a description $\begin{aligned} A middle school surveyed 95 sixth and seventh graders about pets. 29 students do not have a pet. Of these, 2 are seventh graders. Also, 11 sixth graders have one. Complete the two-way table. \\ \begin{array}{lccc} Pet & No pet & Total \\ Sixth graders \\ Seventh graders \\ Total \end{array} \end{aligned}$ Sixth graders: $11$ have a pet, $27$ do not, $38$ in all. Seventh graders: $55$ have a pet, $2$ do not, $57$ in all. Totals: $66$ have a pet, $29$ do not, $95$ in all. $\begin{aligned} A music teacher surveyed 85 juniors and seniors about whether they play an instrument. Of the juniors, 40 play one and 15 do not play one. In all, 41 do not play an instrument. Complete the two-way table. \\ \begin{array}{lccc} Instrument & None & Total \\ Juniors \\ Seniors \\ Total \end{array} \end{aligned}$ Juniors: $40$ play an instrument, $15$ do not, $55$ in all. Seniors: $4$ play an instrument, $26$ do not, $30$ in all. Totals: $44$ play an instrument, $41$ do not, $85$ in all. Find a conditional percent $\begin{aligned} What percent of the cars are hybrid? Round to the nearest tenth. \\ \begin{array}{lccc} Electric & Gas & Hybrid \\ Car & 39 & 38 & 29 \\ Truck & 37 & 34 & 38 \end{array} \end{aligned}$ $27.4 %$ $\begin{aligned} What percent of the hybrid vehicles are cars? Round to the nearest tenth. \\ \begin{array}{lccc} Electric & Gas & Hybrid \\ Car & 11 & 6 & 8 \\ Truck & 18 & 23 & 13 \end{array} \end{aligned}$ $38.1 %$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Two-Way TablesAnswer keyVersion 1

Date Period

Use each table.

Fill in the missing value
$\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 3 & __ & 15 \\ Trucks & 20 & 20 & 40 \\ Total & 23 & 32 & 55 \end{array} \end{aligned}$ $12$
$\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & __ & 12 & 30 \\ Sophomores & 19 & 15 & 34 \\ Total & 37 & 27 & 64 \end{array} \end{aligned}$ $18$
$\begin{aligned} Fill in the missing value. \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 14 & __ & 29 \\ Weekend shoppers & 7 & 9 & 16 \\ Total & 21 & 24 & 45 \end{array} \end{aligned}$ $15$

Find a fraction of the whole table
$\begin{aligned} What fraction of the vehicles are Cars and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 30 & 19 & 49 \\ Trucks & 40 & 20 & 60 \\ Total & 70 & 39 & 109 \end{array} \end{aligned}$ $\frac{19}{109}$
$\begin{aligned} What fraction of the pets are Dogs and 5 and over? \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 39 & 8 & 47 \\ Cats & 40 & 9 & 49 \\ Total & 79 & 17 & 96 \end{array} \end{aligned}$ $\frac{1}{12}$
$\begin{aligned} What fraction of the students are Freshmen and No phone? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 13 & 38 & 51 \\ Sophomores & 39 & 9 & 48 \\ Total & 52 & 47 & 99 \end{array} \end{aligned}$ $\frac{38}{99}$

Find a percent of the whole table
$\begin{aligned} What percent of the students are Boys and Athletes? \\ \begin{array}{lcc} Athletes & Non-athletes \\ Boys & 7 & 8 \\ Girls & 2 & 3 \end{array} \end{aligned}$ $35 %$
$\begin{aligned} What percent of the students are Boys and Non-athletes? \\ \begin{array}{lcc} Athletes & Non-athletes \\ Boys & 5 & 34 \\ Girls & 8 & 3 \end{array} \end{aligned}$ $68 %$

Find a conditional relative frequency
$\begin{aligned} What fraction of the Girls are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 10 & 13 & 23 \\ Girls & 17 & 8 & 25 \\ Total & 27 & 21 & 48 \end{array} \end{aligned}$ $\frac{8}{25}$
$\begin{aligned} What fraction of the Athletes are Girls? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 8 & 19 & 27 \\ Girls & 8 & 5 & 13 \\ Total & 16 & 24 & 40 \end{array} \end{aligned}$ $\frac{1}{2}$

Find a marginal percent
$\begin{aligned} What percent of the adults are in the Coffee column? \\ Round to the nearest percent. \\ \begin{array}{lccc} Coffee & Tea & Total \\ Under 30 & 10 & 30 & 40 \\ 30 and over & 20 & 32 & 52 \\ Total & 30 & 62 & 92 \end{array} \end{aligned}$ $33 %$
$\begin{aligned} What percent of the vehicles are in the Electric column? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 8 & 5 & 13 \\ Trucks & 14 & 28 & 42 \\ Total & 22 & 33 & 55 \end{array} \end{aligned}$ $40 %$

Decide if there is an association
$\begin{aligned} Is there an association? Compare each row’s \\ percent in the Electric column. \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 10 & 15 & 25 \\ Trucks & 20 & 5 & 25 \\ Total & 30 & 20 & 50 \end{array} \end{aligned}$ Yes: $40 %$ of Cars and $80 %$ of Trucks
$\begin{aligned} Is there an association? Compare each row’s \\ percent in the Indoor column. \\ \begin{array}{lccc} Indoor & Outdoor & Total \\ Cats & 20 & 20 & 40 \\ Dogs & 15 & 5 & 20 \\ Total & 35 & 25 & 60 \end{array} \end{aligned}$ Yes: $50 %$ of Cats and $75 %$ of Dogs

Decide if the events are independent
$\begin{aligned} Are the events “Drive” and “Seniors” independent? \\ Round each probability to the nearest hundredth before you compare. \\ \begin{array}{lcc} Drive & Bus \\ Juniors & 18 & 12 \\ Seniors & 12 & 8 \end{array} \end{aligned}$ Yes: $P ($ Drive $∣$ Seniors $) = 0.60 = P ($ Drive $)$
$\begin{aligned} Are the events “Coffee” and “Teens” independent? \\ Round each probability to the nearest hundredth before you compare. \\ \begin{array}{lcc} Coffee & Tea \\ Adults & 4 & 16 \\ Teens & 9 & 16 \end{array} \end{aligned}$ No: $P ($ Coffee $∣$ Teens $) = 0.36$ , but $P ($ Coffee $) = 0.29$

Build the two-way table from a description
$\begin{aligned} A middle school surveyed 95 sixth and seventh graders about pets. 29 students do not have a pet. Of these, 2 are seventh graders. Also, 11 sixth graders have one. Complete the two-way table. \\ \begin{array}{lccc} Pet & No pet & Total \\ Sixth graders \\ Seventh graders \\ Total \end{array} \end{aligned}$ Sixth graders: $11$ have a pet, $27$ do not, $38$ in all. Seventh graders: $55$ have a pet, $2$ do not, $57$ in all. Totals: $66$ have a pet, $29$ do not, $95$ in all.
$\begin{aligned} A music teacher surveyed 85 juniors and seniors about whether they play an instrument. Of the juniors, 40 play one and 15 do not play one. In all, 41 do not play an instrument. Complete the two-way table. \\ \begin{array}{lccc} Instrument & None & Total \\ Juniors \\ Seniors \\ Total \end{array} \end{aligned}$ Juniors: $40$ play an instrument, $15$ do not, $55$ in all. Seniors: $4$ play an instrument, $26$ do not, $30$ in all. Totals: $44$ play an instrument, $41$ do not, $85$ in all.

Find a conditional percent
$\begin{aligned} What percent of the cars are hybrid? Round to the nearest tenth. \\ \begin{array}{lccc} Electric & Gas & Hybrid \\ Car & 39 & 38 & 29 \\ Truck & 37 & 34 & 38 \end{array} \end{aligned}$ $27.4 %$
$\begin{aligned} What percent of the hybrid vehicles are cars? Round to the nearest tenth. \\ \begin{array}{lccc} Electric & Gas & Hybrid \\ Car & 11 & 6 & 8 \\ Truck & 18 & 23 & 13 \end{array} \end{aligned}$ $38.1 %$

How to do these

What fraction of the Boys are Athletes? $\begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 12 & 8 & 20 \\ Girls & 9 & 11 & 20 \\ Total & 21 & 19 & 40 \end{array}$

"Of the boys" means the boys row is the whole.
12 of the 20 boys are athletes.

The answer is $\frac{3}{5}$ .

Where students go wrong

Dividing by the grand total when the question narrows to one row. 12 out of 40 answers a different question from 12 out of 20.

Also called two-way tables, relative frequency, conditional relative frequency or joint and marginal frequency.

What you can put on this worksheet

Fill in the missing value: Fill in the missing value.
$\begin{array}{lccc} Electric & Gas & Total \\ Cars & 13 & 16 & 29 \\ Trucks & __ & 11 & 15 \\ Total & 17 & 27 & 44 \end{array}$ → $4$
A fraction of the whole table: What fraction of the vehicles are Trucks and Electric?
$\begin{array}{lccc} Electric & Gas & Total \\ Cars & 13 & 16 & 29 \\ Trucks & 4 & 11 & 15 \\ Total & 17 & 27 & 44 \end{array}$ → $\frac{1}{11}$
A percent of the whole table: What percent of the vehicles are Trucks and Gas?
$\begin{array}{lccc} Electric & Gas & Total \\ Cars & 12 & 33 & 45 \\ Trucks & 2 & 3 & 5 \\ Total & 14 & 36 & 50 \end{array}$ → $6 %$
A fraction of one row or column: What fraction of the Gas are Cars?
$\begin{array}{lccc} Electric & Gas & Total \\ Cars & 13 & 16 & 29 \\ Trucks & 4 & 11 & 15 \\ Total & 17 & 27 & 44 \end{array}$ → $\frac{16}{27}$
A row or column total as a percent: What percent of the pets are in the Indoor column?
Round to the nearest percent.
$\begin{array}{lccc} Indoor & Outdoor & Total \\ Cats & 24 & 30 & 54 \\ Dogs & 5 & 21 & 26 \\ Total & 29 & 51 & 80 \end{array}$ → $36 %$
Is there an association?: Is there an association? Compare each row's
percent in the Indoor column.
$\begin{array}{lccc} Indoor & Outdoor & Total \\ Cats & 8 & 32 & 40 \\ Dogs & 32 & 8 & 40 \\ Total & 40 & 40 & 80 \end{array}$ → Yes: $20 %$ of Cats and $80 %$ of Dogs
Are the events independent?: Are the events “Drive” and “Seniors” independent?
Round each probability to the nearest hundredth before you compare.
$\begin{array}{lcc} Drive & Bus \\ Juniors & 20 & 30 \\ Seniors & 12 & 8 \end{array}$ → No: $P ($ Drive $∣$ Seniors $) = 0.60$ , but $P ($ Drive $) = 0.46$
Build the table from a description: 70 sixth and seventh graders were asked whether they have a pet. 33 sixth graders have a pet, and 4 sixth graders do not have one. Of the seventh graders, 23 have one. Complete the two-way table.
$\begin{array}{lccc} Pet & No pet & Total \\ Sixth graders \\ Seventh graders \\ Total \end{array}$ → Sixth graders: $33$ have a pet, $4$ do not, $37$ in all. Seventh graders: $23$ have a pet, $10$ do not, $33$ in all. Totals: $56$ have a pet, $14$ do not, $70$ in all.
A percent of one row or column: What percent of the cars are hybrid? Round to the nearest tenth.
$\begin{array}{lccc} Electric & Gas & Hybrid \\ Car & 23 & 24 & 30 \\ Truck & 5 & 21 & 24 \end{array}$ → $39.0 %$

Questions about these worksheets

Yes. Every two-way frequency tables sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the two-way frequency tables questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 9: fill in the missing value, a fraction of the whole table, a percent of the whole table, a fraction of one row or column, a row or column total as a percent, is there an association?, are the events independent?, build the table from a description and a percent of one row or column. Tick as many as you want and set how many of each, or let it spread them evenly.

Dividing by the grand total when the question narrows to one row. 12 out of 40 answers a different question from 12 out of 20.

Two-way frequency tables worksheet for Statistics

Fill in the missing value

Find a fraction of the whole table

Find a percent of the whole table

Find a conditional relative frequency

Find a marginal percent

Decide if there is an association

Decide if the events are independent

Build the two-way table from a description

Find a conditional percent

Fill in the missing value

Find a fraction of the whole table

Find a percent of the whole table

Find a conditional relative frequency

Find a marginal percent

Decide if there is an association

Decide if the events are independent

Build the two-way table from a description

Find a conditional percent

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these two-way frequency tables worksheets free?+

Do the two-way frequency tables worksheets come with an answer key?+

Are these two-way frequency tables worksheets printable?+

What grade are these two-way frequency tables worksheets for?+

Can I get a different version of the same two-way frequency tables worksheet?+

Is this a free alternative to Kuta Software for two-way frequency tables?+

Can I choose how hard the two-way frequency tables questions are?+

What kinds of question are on a two-way frequency tables worksheet?+

What do students get wrong with two-way frequency tables?+