Testinar Grade 8 math

Two-Way Tables for Categorical Data

Learn to reason about and solve Grade 8 problems involving Two-Way Tables for Categorical Data.

CH06-04 Statistics, Data, and Probability

Name
Date
Score: ____ / 8

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

A two-way table shows that \(30\) students like pizza and \(20\) like sandwiches. \(15\) of those who like pizza are girls. What is the relative frequency of girls among pizza-likers?
1. \(50\%\)
2. \(60\%\)
3. \(30\%\)
4. \(75\%\)
The table below shows preferences for sports among 100 students. How many boys prefer basketball?
1. 15
2. 20
3. 35
4. 50
A two-way table of \(120\) people shows: What is the joint frequency of rural people who own a car?
1. \(\frac{60}{120}\)
2. \(\frac{45}{60}\)
3. \(\frac{45}{120}\)
4. \(\frac{45}{69}\)
A two-way table categorizes 150 households by income level and internet access: Among high-income households, what is the relative frequency of those without internet, as a decimal?
1. \(0.033\)
2. \(0.083\)
3. \(0.367\)
4. \(0.917\)
A two-way table shows 160 athletes: What percentage of all athletes train in the morning on the track team?
1. \(31.25\%\)
2. \(37.5\%\)
3. \(58.8\%\)
4. \(62.5\%\)
A school newsletter reports that 250 students were surveyed about lunch preferences. The two-way table shows: What is the marginal frequency for middle school students?
1. 55
2. 70
3. 115
4. 125
A two-way table with 280 people: Among those who own a phone, what is the relative frequency for ages 13--17, rounded to the nearest hundredth?
1. \(0.62\)
2. \(0.69\)
3. \(0.78\)
4. \(0.89\)
A two-way table tracks 400 students by extracurricular activity: What is the marginal relative frequency for students who do sports, as a decimal?
1. \(0.27\)
2. \(0.45\)
3. \(0.55\)
4. \(0.73\)

Teacher and parent reference

Answer key and explanations

A. \(50\%\)
This is a row-conditional relative frequency. Among pizza-likers (30 total), 15 are girls: \(\frac{15}{30}=0.5=50\%\).
B. 20
This is a joint frequency (read directly from the cell). Row label Boys, column Basketball: entry is 20.
C. \(\frac{45}{120}\)
Joint frequency: intersection cell (45) divided by grand total (120). This answers 'what fraction of all respondents are rural car-owners?' = \(\frac{45}{120}\approx0.375\).
B. \(0.083\)
Among high-income households (total 60), those without internet = 5. Relative frequency = \(\frac{5}{60}\approx0.083\).
A. \(31.25\%\)
Joint frequency of morning track athletes: \(\frac{50}{160}=0.3125=31.25\%\).
D. 125
The marginal frequency for middle school is the row total: \(55+70=125\).
B. \(0.69\)
This is a column-conditional frequency. Among phone owners (253 total), ages 13--17 number 175. Relative frequency: \(\frac{175}{253}\approx0.69\).
C. \(0.55\)
Marginal relative frequency for sports: \(\frac{220}{400}=0.55\). This is the column-total ratio.