Question

for the soccer banquet, the players and their family members selected their favorite main dish and side dish. of the 39 people who chose chicken as the main dish, 18 wanted potatoes. of the 32 people who chose rice as a side dish, 6 chose fish as a main dish. a total of 8 people chose a vegetarian meal with potatoes, and a total of 10 people chose fish as their main dish.

which two-way table correctly displays this data?

Explanation:

Extract the given data values

Using the Two-Way Frequency Tables knowledge point

• Total Chicken main dish = \(39\)
• Chicken with Potatoes = \(18\)
• Total Rice side dish = \(32\)
• Fish with Rice = \(6\)
• Vegetarian with Potatoes = \(8\)
• Total Fish main dish = \(10\)

Calculate the remaining table values

Using the Two-Way Frequency Tables knowledge point

• Chicken with Rice:

$$ \text{Chicken with Rice} = \text{Total Chicken} - \text{Chicken with Potatoes} = 39 - 18 = 21 $$

• Fish with Potatoes:

$$ \text{Fish with Potatoes} = \text{Total Fish} - \text{Fish with Rice} = 10 - 6 = 4 $$

• Total Potatoes side dish:

$$ \text{Total Potatoes} = \text{Chicken with Potatoes} + \text{Fish with Potatoes} + \text{Vegetarian with Potatoes} = 18 + 4 + 8 = 30 $$

• Vegetarian with Rice:

$$ \text{Vegetarian with Rice} = \text{Total Rice} - \text{Chicken with Rice} - \text{Fish with Rice} = 32 - 21 - 6 = 5 $$

• Total Vegetarian main dish:

$$ \text{Total Vegetarian} = \text{Vegetarian with Rice} + \text{Vegetarian with Potatoes} = 5 + 8 = 13 $$

• Grand Total:

$$ \text{Grand Total} = \text{Total Rice} + \text{Total Potatoes} = 32 + 30 = 62 $$

Match with the given options

Using the Two-Way Frequency Tables knowledge point

• Option 1: Rice row has Chicken = 18, Fish = 4, Vegetarian = 8. (Incorrect)
• Option 2: Rice row has Chicken = 21, Fish = 6, Vegetarian = 5, Total = 32. Potatoes row has Chicken = 18, Fish = 4, Vegetarian = 8, Total = 30. Total row has Chicken = 39, Fish = 10, Vegetarian = 13, Total = 62. (Correct)
• Option 3: Total Chicken is listed as 32. (Incorrect)
• Option 4: Total Chicken is listed as 32. (Incorrect)

Answer:

• (A) Table 1 (Rice: Chicken=18, Fish=4, Vegetarian=8, Total=30; Potatoes: Chicken=21, Fish=6, Vegetarian=5, Total=32)
• (B) Table 2 (Rice: Chicken=21, Fish=6, Vegetarian=5, Total=32; Potatoes: Chicken=18, Fish=4, Vegetarian=8, Total=30) (Correct answer)
• (C) Table 3 (Rice: Chicken=14, Fish=6, Vegetarian=19, Total=39; Potatoes: Chicken=18, Fish=4, Vegetarian=8, Total=30)
• (D) Table 4 (Rice: Chicken=18, Fish=4, Vegetarian=8, Total=30; Potatoes: Chicken=14, Fish=6, Vegetarian=10, Total=30)