Question

a two - way frequency table contains data about the method students use to travel to school and their age.
which category has the lowest joint frequency?

	walk/bike	bus	car	total
age 15 and above			60	195
total	152	100	110	362

options:

• students that are under the age of 15 and travel to school in a car
• students that are above the age of 15 and travel to school in a bus
• students that are under the age of 15
• students who take the bus to school

Explanation:

Step1: Calculate under-age-15 for each category

• Walk/Bike: 65 (given)
• Bus: Total Bus (100) - Age 15+ Bus. First, find total under age 15: Total (362) - Age 15+ (195) = 167. Then Bus under 15: 167 - 65 (Walk/Bike under 15) - (110 - 60) (Car under 15, since Car total 110, Age 15+ 60, so under 15 is 50) = 167 - 65 - 50 = 52
• Car: 110 - 60 = 50
• Check: 65 + 52 + 50 = 167 (matches total under 15: 362 - 195 = 167)

Step2: Calculate age-15+ for each category

• Walk/Bike: 152 - 65 = 87
• Bus: 100 - 52 = 48
• Car: 60 (given)
• Check: 87 + 48 + 60 = 195 (matches age 15+ total)

Step3: Analyze each option

• "Students that are under the age of 15 and travel to school in a car": 50
• "Students that are above the age of 15 and travel to school in a bus": 48
• "Students that are under the age of 15": 167 (total, not joint)
• "Students who take the bus to school": 100 (total, not joint)

Compare joint frequencies: 48 (Bus, Age 15+), 50 (Car, under 15), 65 (Walk/Bike, under 15), 87 (Walk/Bike, Age 15+), 52 (Bus, under 15), 60 (Car, Age 15+). The lowest is 48, which is "Students that are above the age of 15 and travel to school in a bus".

Answer:

Students that are above the age of 15 and travel to school in a bus