select the correct answer.

josh works as a server at a restaurant. the given data set shows the amount of gratuity, in dollars, that he earned from each table that he served on a given night.

10, 8, 50, 15, 10, 25, 20, 5, 12, 15, 20, 15, 25, 18, 20

which box plot represents the data set?

Question

select the correct answer.

josh works as a server at a restaurant. the given data set shows the amount of gratuity, in dollars, that he earned from each table that he served on a given night.

10, 8, 50, 15, 10, 25, 20, 5, 12, 15, 20, 15, 25, 18, 20

which box plot represents the data set?

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": [ "Box Plots", "Five-Number Summary" ], "current_concepts": [ "Box Plots", "Five-Number Summary", "Median Calculation" ] } ## Order the data set $$ 5, 8, 10, 10, 12, 15, 15, 15, 18, 20, 20, 20, 25, 25, 50 $$ ## Calculate the five-number summary $$ \begin{aligned} &\text{Minimum} = 5\ &\text{Maximum} = 50\ &N = 15\ &\text{Median } (Q_2) = \text{8th value} = 15\ &\text{Lower Half: } 5, 8, 10, 10, 12, 15, 15 \implies Q_1 = \text{4th value} = 10\ &\text{Upper Half: } 18, 20, 20, 20, 25, 25, 50 \implies Q_3 = \text{12th value} = 20 \end{aligned} $$ ## Match with the correct box plot $$ \begin{aligned} &\text{Five-number summary: } [5, 10, 15, 20, 50]\ &\text{Plot W has: Min}=5, Q_1=10, \text{Median}=15, Q_3=20, \text{Max}=50\ &\text{Plot X has: Min}=5, Q_1=10, \text{Median}=15, Q_3=25, \text{Max}=50 \end{aligned} $$

(A) W.

(B) X.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Box Plots" ] }

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QUESTION IMAGE

Question

Explanation:

Order the data set

Calculate the five-number summary

Match with the correct box plot

Answer: