question 17 (5 points)

the box plot shown represents the heights of 200 students. approximately how many of these students are between 37 and 46.5 inches tall?

100 students
150 students
50 students
180 students

Question

question 17 (5 points)

the box plot shown represents the heights of 200 students. approximately how many of these students are between 37 and 46.5 inches tall?

100 students
150 students
50 students
180 students

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Five-Number Summary", "Box-and-Whisker Plot" ], "new_concepts": [], "current_concepts": [ "Five-Number Summary", "Box-and-Whisker Plot", "Interquartile Range", "Percentiles" ] } ## Identify key values from the box plot $$ \begin{aligned} &\text{Minimum} = 37 \ &\text{First Quartile } (Q_1) = 41.5 \ &\text{Median } (Q_2) = 43.5 \ &\text{Third Quartile } (Q_3) = 46.5 \ &\text{Maximum} = 50 \end{aligned} $$ ## Determine the percentage of data in the interval $$ \begin{aligned} &\text{Interval: } [37, 46.5] \implies [\text{Minimum}, Q_3] \ &\text{Percentage of data below } Q_3 = 75\% \end{aligned} $$ ## Calculate the number of students $$ \begin{aligned} &\text{Total Students } (N) = 200 \ &\text{Number of Students} = 200 \times 0.75 = 150 \end{aligned} $$

100 students

150 students

50 students

180 students

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Box-and-Whisker Plot" ] }

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QUESTION IMAGE

Question

Explanation:

Identify key values from the box plot

Determine the percentage of data in the interval

Calculate the number of students

Answer: