Two-way frequency tables worksheet

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.



Sigma Prep · sigmaprep.io/worksheets Name Two‑Way Tables Date Period Use each table. $\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 3 & 23 & 26 \\ Trucks & 40 & 39 & __ \\ Total & 43 & 62 & 105 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the vehicles are Cars and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 30 & 19 & 49 \\ Trucks & 40 & 20 & 60 \\ Total & 70 & 39 & 109 \end{array} \end{aligned}$ $\begin{aligned} What percent of the students are Boys and Athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 7 & 8 & 15 \\ Girls & 2 & 3 & 5 \\ Total & 9 & 11 & 20 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the Girls are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 19 & 25 & 44 \\ Girls & 33 & 14 & 47 \\ Total & 52 & 39 & 91 \end{array} \end{aligned}$ $\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 10 & 30 & 40 \\ Cats & 20 & 32 & 52 \\ Total & 30 & __ & 92 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the students are Freshmen and Phone owners? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 31 & 8 & 39 \\ Sophomores & 15 & 18 & 33 \\ Total & 46 & 26 & 72 \end{array} \end{aligned}$ $\begin{aligned} What percent of the students are Girls and Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 10 & 6 & 16 \\ Girls & 2 & 2 & 4 \\ Total & 12 & 8 & 20 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the 5 and over are Cats? \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 18 & 14 & 32 \\ Cats & 28 & 39 & 67 \\ Total & 46 & 53 & 99 \end{array} \end{aligned}$ $\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 38 & 7 & 45 \\ Weekend shoppers & 4 & 36 & __ \\ Total & 42 & 43 & 85 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the customers are Weekend shoppers and Cash payers? \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 22 & 38 & 60 \\ Weekend shoppers & 29 & 9 & 38 \\ Total & 51 & 47 & 98 \end{array} \end{aligned}$ $\begin{aligned} What percent of the customers are Weekend shoppers and Cash payers? \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 7 & 4 & 11 \\ Weekend shoppers & 5 & 4 & 9 \\ Total & 12 & 8 & 20 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the Cars are Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 5 & 33 & 38 \\ Trucks & 35 & 13 & 48 \\ Total & 40 & 46 & 86 \end{array} \end{aligned}$ $\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 8 & 27 & __ \\ Sophomores & 23 & 15 & 38 \\ Total & 31 & 42 & 73 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the students are Boys and Athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 5 & 14 & 19 \\ Girls & 28 & 27 & 55 \\ Total & 33 & 41 & 74 \end{array} \end{aligned}$ $\begin{aligned} What percent of the vehicles are Cars and Electric? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 233 & 12 & 245 \\ Trucks & 2 & 3 & 5 \\ Total & 235 & 15 & 250 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the Boys are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 40 & 15 & 55 \\ Girls & 30 & 35 & 65 \\ Total & 70 & 50 & 120 \end{array} \end{aligned}$ $\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 33 & 11 & 44 \\ Cats & 6 & 8 & __ \\ Total & 39 & 19 & 58 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the vehicles are Trucks and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 13 & 36 & 49 \\ Trucks & 14 & 37 & 51 \\ Total & 27 & 73 & 100 \end{array} \end{aligned}$ $\begin{aligned} What percent of the vehicles are Cars and Electric? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 6 & 15 & 21 \\ Trucks & 2 & 2 & 4 \\ Total & 8 & 17 & 25 \end{array} \end{aligned}$ $\begin{aligned} What fraction of the Freshmen are No phone? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 5 & 4 & 9 \\ Sophomores & 32 & 17 & 49 \\ Total & 37 & 21 & 58 \end{array} \end{aligned}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Two‑Way Tables

Date Period

Use each table.

$\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 3 & 23 & 26 \\ Trucks & 40 & 39 & __ \\ Total & 43 & 62 & 105 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the vehicles are Cars and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 30 & 19 & 49 \\ Trucks & 40 & 20 & 60 \\ Total & 70 & 39 & 109 \end{array} \end{aligned}$
$\begin{aligned} What percent of the students are Boys and Athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 7 & 8 & 15 \\ Girls & 2 & 3 & 5 \\ Total & 9 & 11 & 20 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the Girls are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 19 & 25 & 44 \\ Girls & 33 & 14 & 47 \\ Total & 52 & 39 & 91 \end{array} \end{aligned}$
$\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 10 & 30 & 40 \\ Cats & 20 & 32 & 52 \\ Total & 30 & __ & 92 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the students are Freshmen and Phone owners? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 31 & 8 & 39 \\ Sophomores & 15 & 18 & 33 \\ Total & 46 & 26 & 72 \end{array} \end{aligned}$
$\begin{aligned} What percent of the students are Girls and Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 10 & 6 & 16 \\ Girls & 2 & 2 & 4 \\ Total & 12 & 8 & 20 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the 5 and over are Cats? \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 18 & 14 & 32 \\ Cats & 28 & 39 & 67 \\ Total & 46 & 53 & 99 \end{array} \end{aligned}$
$\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 38 & 7 & 45 \\ Weekend shoppers & 4 & 36 & __ \\ Total & 42 & 43 & 85 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the customers are Weekend shoppers and Cash payers? \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 22 & 38 & 60 \\ Weekend shoppers & 29 & 9 & 38 \\ Total & 51 & 47 & 98 \end{array} \end{aligned}$
$\begin{aligned} What percent of the customers are Weekend shoppers and Cash payers? \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 7 & 4 & 11 \\ Weekend shoppers & 5 & 4 & 9 \\ Total & 12 & 8 & 20 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the Cars are Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 5 & 33 & 38 \\ Trucks & 35 & 13 & 48 \\ Total & 40 & 46 & 86 \end{array} \end{aligned}$
$\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 8 & 27 & __ \\ Sophomores & 23 & 15 & 38 \\ Total & 31 & 42 & 73 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the students are Boys and Athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 5 & 14 & 19 \\ Girls & 28 & 27 & 55 \\ Total & 33 & 41 & 74 \end{array} \end{aligned}$
$\begin{aligned} What percent of the vehicles are Cars and Electric? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 233 & 12 & 245 \\ Trucks & 2 & 3 & 5 \\ Total & 235 & 15 & 250 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the Boys are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 40 & 15 & 55 \\ Girls & 30 & 35 & 65 \\ Total & 70 & 50 & 120 \end{array} \end{aligned}$
$\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 33 & 11 & 44 \\ Cats & 6 & 8 & __ \\ Total & 39 & 19 & 58 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the vehicles are Trucks and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 13 & 36 & 49 \\ Trucks & 14 & 37 & 51 \\ Total & 27 & 73 & 100 \end{array} \end{aligned}$
$\begin{aligned} What percent of the vehicles are Cars and Electric? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 6 & 15 & 21 \\ Trucks & 2 & 2 & 4 \\ Total & 8 & 17 & 25 \end{array} \end{aligned}$
$\begin{aligned} What fraction of the Freshmen are No phone? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 5 & 4 & 9 \\ Sophomores & 32 & 17 & 49 \\ Total & 37 & 21 & 58 \end{array} \end{aligned}$



Sigma Prep · sigmaprep.io/worksheets Name Two‑Way TablesAnswer keyVersion 1 Date Period Use each table. $\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 3 & 23 & 26 \\ Trucks & 40 & 39 & __ \\ Total & 43 & 62 & 105 \end{array} \end{aligned}$ $79$ $\begin{aligned} What fraction of the vehicles are Cars and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 30 & 19 & 49 \\ Trucks & 40 & 20 & 60 \\ Total & 70 & 39 & 109 \end{array} \end{aligned}$ $\frac{19}{109}$ $\begin{aligned} What percent of the students are Boys and Athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 7 & 8 & 15 \\ Girls & 2 & 3 & 5 \\ Total & 9 & 11 & 20 \end{array} \end{aligned}$ $35 %$ $\begin{aligned} What fraction of the Girls are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 19 & 25 & 44 \\ Girls & 33 & 14 & 47 \\ Total & 52 & 39 & 91 \end{array} \end{aligned}$ $\frac{14}{47}$ $\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 10 & 30 & 40 \\ Cats & 20 & 32 & 52 \\ Total & 30 & __ & 92 \end{array} \end{aligned}$ $62$ $\begin{aligned} What fraction of the students are Freshmen and Phone owners? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 31 & 8 & 39 \\ Sophomores & 15 & 18 & 33 \\ Total & 46 & 26 & 72 \end{array} \end{aligned}$ $\frac{31}{72}$ $\begin{aligned} What percent of the students are Girls and Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 10 & 6 & 16 \\ Girls & 2 & 2 & 4 \\ Total & 12 & 8 & 20 \end{array} \end{aligned}$ $10 %$ $\begin{aligned} What fraction of the 5 and over are Cats? \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 18 & 14 & 32 \\ Cats & 28 & 39 & 67 \\ Total & 46 & 53 & 99 \end{array} \end{aligned}$ $\frac{39}{53}$ $\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 38 & 7 & 45 \\ Weekend shoppers & 4 & 36 & __ \\ Total & 42 & 43 & 85 \end{array} \end{aligned}$ $40$ $\begin{aligned} What fraction of the customers are Weekend shoppers and Cash payers? \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 22 & 38 & 60 \\ Weekend shoppers & 29 & 9 & 38 \\ Total & 51 & 47 & 98 \end{array} \end{aligned}$ $\frac{29}{98}$ $\begin{aligned} What percent of the customers are Weekend shoppers and Cash payers? \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 7 & 4 & 11 \\ Weekend shoppers & 5 & 4 & 9 \\ Total & 12 & 8 & 20 \end{array} \end{aligned}$ $25 %$ $\begin{aligned} What fraction of the Cars are Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 5 & 33 & 38 \\ Trucks & 35 & 13 & 48 \\ Total & 40 & 46 & 86 \end{array} \end{aligned}$ $\frac{33}{38}$ $\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 8 & 27 & __ \\ Sophomores & 23 & 15 & 38 \\ Total & 31 & 42 & 73 \end{array} \end{aligned}$ $35$ $\begin{aligned} What fraction of the students are Boys and Athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 5 & 14 & 19 \\ Girls & 28 & 27 & 55 \\ Total & 33 & 41 & 74 \end{array} \end{aligned}$ $\frac{5}{74}$ $\begin{aligned} What percent of the vehicles are Cars and Electric? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 233 & 12 & 245 \\ Trucks & 2 & 3 & 5 \\ Total & 235 & 15 & 250 \end{array} \end{aligned}$ $93.2 %$ $\begin{aligned} What fraction of the Boys are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 40 & 15 & 55 \\ Girls & 30 & 35 & 65 \\ Total & 70 & 50 & 120 \end{array} \end{aligned}$ $\frac{3}{11}$ $\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 33 & 11 & 44 \\ Cats & 6 & 8 & __ \\ Total & 39 & 19 & 58 \end{array} \end{aligned}$ $14$ $\begin{aligned} What fraction of the vehicles are Trucks and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 13 & 36 & 49 \\ Trucks & 14 & 37 & 51 \\ Total & 27 & 73 & 100 \end{array} \end{aligned}$ $\frac{37}{100}$ $\begin{aligned} What percent of the vehicles are Cars and Electric? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 6 & 15 & 21 \\ Trucks & 2 & 2 & 4 \\ Total & 8 & 17 & 25 \end{array} \end{aligned}$ $24 %$ $\begin{aligned} What fraction of the Freshmen are No phone? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 5 & 4 & 9 \\ Sophomores & 32 & 17 & 49 \\ Total & 37 & 21 & 58 \end{array} \end{aligned}$ $\frac{4}{9}$ 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.

$\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 3 & 23 & 26 \\ Trucks & 40 & 39 & __ \\ Total & 43 & 62 & 105 \end{array} \end{aligned}$ $79$
$\begin{aligned} What fraction of the vehicles are Cars and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 30 & 19 & 49 \\ Trucks & 40 & 20 & 60 \\ Total & 70 & 39 & 109 \end{array} \end{aligned}$ $\frac{19}{109}$
$\begin{aligned} What percent of the students are Boys and Athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 7 & 8 & 15 \\ Girls & 2 & 3 & 5 \\ Total & 9 & 11 & 20 \end{array} \end{aligned}$ $35 %$
$\begin{aligned} What fraction of the Girls are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 19 & 25 & 44 \\ Girls & 33 & 14 & 47 \\ Total & 52 & 39 & 91 \end{array} \end{aligned}$ $\frac{14}{47}$
$\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 10 & 30 & 40 \\ Cats & 20 & 32 & 52 \\ Total & 30 & __ & 92 \end{array} \end{aligned}$ $62$
$\begin{aligned} What fraction of the students are Freshmen and Phone owners? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 31 & 8 & 39 \\ Sophomores & 15 & 18 & 33 \\ Total & 46 & 26 & 72 \end{array} \end{aligned}$ $\frac{31}{72}$
$\begin{aligned} What percent of the students are Girls and Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 10 & 6 & 16 \\ Girls & 2 & 2 & 4 \\ Total & 12 & 8 & 20 \end{array} \end{aligned}$ $10 %$
$\begin{aligned} What fraction of the 5 and over are Cats? \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 18 & 14 & 32 \\ Cats & 28 & 39 & 67 \\ Total & 46 & 53 & 99 \end{array} \end{aligned}$ $\frac{39}{53}$
$\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 38 & 7 & 45 \\ Weekend shoppers & 4 & 36 & __ \\ Total & 42 & 43 & 85 \end{array} \end{aligned}$ $40$
$\begin{aligned} What fraction of the customers are Weekend shoppers and Cash payers? \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 22 & 38 & 60 \\ Weekend shoppers & 29 & 9 & 38 \\ Total & 51 & 47 & 98 \end{array} \end{aligned}$ $\frac{29}{98}$
$\begin{aligned} What percent of the customers are Weekend shoppers and Cash payers? \\ \begin{array}{lccc} Cash payers & Card payers & Total \\ Weekday shoppers & 7 & 4 & 11 \\ Weekend shoppers & 5 & 4 & 9 \\ Total & 12 & 8 & 20 \end{array} \end{aligned}$ $25 %$
$\begin{aligned} What fraction of the Cars are Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 5 & 33 & 38 \\ Trucks & 35 & 13 & 48 \\ Total & 40 & 46 & 86 \end{array} \end{aligned}$ $\frac{33}{38}$
$\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 8 & 27 & __ \\ Sophomores & 23 & 15 & 38 \\ Total & 31 & 42 & 73 \end{array} \end{aligned}$ $35$
$\begin{aligned} What fraction of the students are Boys and Athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 5 & 14 & 19 \\ Girls & 28 & 27 & 55 \\ Total & 33 & 41 & 74 \end{array} \end{aligned}$ $\frac{5}{74}$
$\begin{aligned} What percent of the vehicles are Cars and Electric? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 233 & 12 & 245 \\ Trucks & 2 & 3 & 5 \\ Total & 235 & 15 & 250 \end{array} \end{aligned}$ $93.2 %$
$\begin{aligned} What fraction of the Boys are Non-athletes? \\ \begin{array}{lccc} Athletes & Non-athletes & Total \\ Boys & 40 & 15 & 55 \\ Girls & 30 & 35 & 65 \\ Total & 70 & 50 & 120 \end{array} \end{aligned}$ $\frac{3}{11}$
$\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Under 5 years & 5 and over & Total \\ Dogs & 33 & 11 & 44 \\ Cats & 6 & 8 & __ \\ Total & 39 & 19 & 58 \end{array} \end{aligned}$ $14$
$\begin{aligned} What fraction of the vehicles are Trucks and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 13 & 36 & 49 \\ Trucks & 14 & 37 & 51 \\ Total & 27 & 73 & 100 \end{array} \end{aligned}$ $\frac{37}{100}$
$\begin{aligned} What percent of the vehicles are Cars and Electric? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 6 & 15 & 21 \\ Trucks & 2 & 2 & 4 \\ Total & 8 & 17 & 25 \end{array} \end{aligned}$ $24 %$
$\begin{aligned} What fraction of the Freshmen are No phone? \\ \begin{array}{lccc} Phone owners & No phone & Total \\ Freshmen & 5 & 4 & 9 \\ Sophomores & 32 & 17 & 49 \\ Total & 37 & 21 & 58 \end{array} \end{aligned}$ $\frac{4}{9}$

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: $\begin{aligned} e x t F i l l i n t h e m i s s i n g v a l u e \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 13 & 16 & 29 \\ Trucks & __ & 11 & 15 \\ Total & 17 & 27 & 44 \end{array} \end{aligned}$ → $4$
A fraction of the whole table: $\begin{aligned} What fraction of the vehicles are Trucks and Electric? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 13 & 16 & 29 \\ Trucks & 4 & 11 & 15 \\ Total & 17 & 27 & 44 \end{array} \end{aligned}$ → $\frac{1}{11}$
A percent of the whole table: $\begin{aligned} What percent of the vehicles are Trucks and Gas? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 12 & 33 & 45 \\ Trucks & 2 & 3 & 5 \\ Total & 14 & 36 & 50 \end{array} \end{aligned}$ → $6 %$
A fraction of one row or column: $\begin{aligned} What fraction of the Gas are Cars? \\ \begin{array}{lccc} Electric & Gas & Total \\ Cars & 13 & 16 & 29 \\ Trucks & 4 & 11 & 15 \\ Total & 17 & 27 & 44 \end{array} \end{aligned}$ → $\frac{16}{27}$

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 4: fill in the missing value, a fraction of the whole table, a percent of the whole table and a fraction 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

Two‑Way Tables

Two‑Way TablesAnswer keyVersion 1

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?+

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