the upperclassmen at a high school were planning for the schools movie night. they surveyed 195 upperclassmen of which 75 were in 12th grade. the survey also found that 81 students in 11th grade preferred comedy and 60 students preferred horror. which of the following frequency tables summarizes the data?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Two-Way Frequency Tables" ], "new_concepts": [], "current_concepts": [ "Two-Way Frequency Tables" ] } ## Identify given marginal and joint frequencies $$ \begin{aligned} &\text{Total upperclassmen} = 195 \ &\text{12th Grade Total} = 75 \ &\text{11th Grade Total} = 195 - 75 = 120 \ &\text{11th Grade Comedy} = 81 \ &\text{Total Horror} = 60 \ &\text{Total Comedy} = 195 - 60 = 135 \end{aligned} $$ ## Calculate remaining joint frequencies $$ \begin{aligned} &\text{11th Grade Horror} = \text{11th Grade Total} - \text{11th Grade Comedy} = 120 - 81 = 39 \ &\text{12th Grade Comedy} = \text{Total Comedy} - \text{11th Grade Comedy} = 135 - 81 = 54 \ &\text{12th Grade Horror} = \text{Total Horror} - \text{11th Grade Horror} = 60 - 39 = 21 \end{aligned} $$ ## Match with the options $$ \begin{array}{r|cc|c} & \text{Comedy} & \text{Horror} & \text{Total} \ \hline \text{11th Grade} & 81 & 39 & 120 \ \text{12th Grade} & 54 & 21 & 75 \ \hline \text{Total} & 135 & 60 & 195 \end{array} $$ This matches the fourth option (marked with the blue selection dot on the far left).

(A) Table with 11th Grade (81 Comedy, 39 Horror, 120 Total), 12th Grade (15 Comedy, 60 Horror, 75 Total), Total (96 Comedy, 99 Horror, 195 Total)

(B) Table with 11th Grade (81 Comedy, 114 Horror, 195 Total), 12th Grade (15 Comedy, 60 Horror, 75 Total), Total (96 Comedy, 174 Horror, 270 Total)

(C) Table with 11th Grade (81 Comedy, 114 Horror, 195 Total), 12th Grade (60 Comedy, 135 Horror, 195 Total), Total (141 Comedy, 249 Horror, 390 Total)

(D) Table with 11th Grade (81 Comedy, 39 Horror, 120 Total), 12th Grade (54 Comedy, 21 Horror, 75 Total), Total (135 Comedy, 60 Horror, 195 Total)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Two-Way Frequency Tables" ] }

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Question

Explanation:

Identify given marginal and joint frequencies

Calculate remaining joint frequencies

Match with the options

Answer: