which teacher exhibited the most variable year-to-year performance over this 5 year span?
teacher 1
teacher 2
teacher 3
teacher 5

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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": [], "new_concepts": [ "Data Variability", "Line Graph Analysis" ], "current_concepts": [ "Data Variability", "Line Graph Analysis" ] } ## Identify annual performance values for each teacher $$ \begin{aligned} &\text{Teacher 1 (solid black): } [3, 3, 3, 4, 5] \ &\text{Teacher 2 (solid blue): } [1, 4, 2, 4, 1] \ &\text{Teacher 3 (dotted grey): } [5, 2, 2, 1, 1] \ &\text{Teacher 5 (long-dashed purple): } [2, 4, 1, 3, 3] \end{aligned} $$ ## Calculate year-to-year absolute changes $$ \begin{aligned} &\text{Teacher 1: } |3-3| + |3-3| + |4-3| + |5-4| = 0 + 0 + 1 + 1 = 2 \ &\text{Teacher 2: } |4-1| + |2-4| + |4-2| + |1-4| = 3 + 2 + 2 + 3 = 10 \ &\text{Teacher 3: } |2-5| + |2-2| + |1-2| + |1-1| = 3 + 0 + 1 + 0 = 4 \ &\text{Teacher 5: } |4-2| + |1-4| + |3-1| + |3-3| = 2 + 3 + 2 + 0 = 7 \end{aligned} $$ ## Determine the teacher with the highest variability $$ \begin{aligned} &\max(2, 10, 4, 7) = 10 \implies \text{Teacher 2} \end{aligned} $$

Teacher 1

Teacher 2

Teacher 3

Teacher 5

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Data Variability" ] }

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Question

Explanation:

Identify annual performance values for each teacher

Calculate year-to-year absolute changes

Determine the teacher with the highest variability

Answer: