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?

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Categorical Data" ], "new_concepts": [ "Two-Way Frequency Tables" ], "current_concepts": [ "Categorical Data", "Two-Way Frequency Tables" ] } ## Identify given values and constraints $$ \begin{aligned} &\text{Total surveyed} = 195\ &\text{12th Grade Total} = 75\ &\text{11th Grade Total} = 195 - 75 = 120\ &\text{11th Grade Comedy} = 81\ &\text{Total Horror} = 60 \end{aligned} $$ ## Calculate missing table values $$ \begin{aligned} &\text{11th Grade Horror} = \text{11th Grade Total} - \text{11th Grade Comedy} = 120 - 81 = 39\ &\text{12th Grade Horror} = \text{Total Horror} - \text{11th Grade Horror} = 60 - 39 = 21\ &\text{12th Grade Comedy} = \text{12th Grade Total} - \text{12th Grade Horror} = 75 - 21 = 54\ &\text{Total Comedy} = \text{11th Grade Comedy} + \text{12th Grade Comedy} = 81 + 54 = 135 \end{aligned} $$ ## Match with options $$ \begin{array}{c|c|c|c} & \text{Comedy} & \text{Horror} & \text{Total} \ \hline \text{11th Grade} & 81 & 39 & 120 \ \text{12th Grade} & 54 & 21 & 75 \ \hline \text{Total} & 135 & 60 & 195 \end{array} $$ This matches the fourth option.

(A) | | Comedy | Horror | Total | |---|---|---|---| | 11th Grade | 81 | 39 | 120 | | 12th Grade | 15 | 60 | 75 | | Total | 96 | 99 | 195 |

(B) | | Comedy | Horror | Total | |---|---|---|---| | 11th Grade | 81 | 114 | 195 | | 12th Grade | 15 | 60 | 75 | | Total | 96 | 174 | 270 |

(C) | | Comedy | Horror | Total | |---|---|---|---| | 11th Grade | 81 | 114 | 195 | | 12th Grade | 60 | 135 | 195 | | Total | 141 | 249 | 390 |

(D) | | Comedy | Horror | Total | |---|---|---|---| | 11th Grade | 81 | 39 | 120 | | 12th Grade | 54 | 21 | 75 | | Total | 135 | 60 | 195 |

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify given values and constraints

Calculate missing table values

Match with options

Answer: