find the lower limit and upper limit of the outlier of the following box and whisker plot.

$q_1 = 34$ $q_2 = 45$ $q_3 = 60$

lower limit of the outlier = -5, upper limit of the outlier = 99
lower limit of the outlier = -12, upper limit of the outlier = 65

Question

find the lower limit and upper limit of the outlier of the following box and whisker plot.

$q_1 = 34$ $q_2 = 45$ $q_3 = 60$

lower limit of the outlier = -5, upper limit of the outlier = 99
lower limit of the outlier = -12, upper limit of the outlier = 65

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Interquartile Range", "Outlier Limits" ], "new_concepts": [], "current_concepts": [ "Box and Whisker Plot", "Interquartile Range", "Outlier Limits" ] } ## Calculate the Interquartile Range Using the *Interquartile Range* knowledge point $$ \begin{aligned} Q_1 &= 34 \ Q_3 &= 60 \ \text{IQR} &= Q_3 - Q_1 = 60 - 34 = 26 \end{aligned} $$ ## Determine the Outlier Limits Using the *Outlier Limits* knowledge point $$ \begin{aligned} \text{Lower Limit} &= Q_1 - 1.5 \times \text{IQR} = 34 - 1.5 \times 26 = 34 - 39 = -5 \ \text{Upper Limit} &= Q_3 + 1.5 \times \text{IQR} = 60 + 1.5 \times 26 = 60 + 39 = 99 \end{aligned} $$

Lower limit of the outlier = -5, Upper limit of the outlier = 99

Lower limit of the outlier = -12, Upper limit of the outlier = 65

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Outlier Limits" ] }

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Question

Explanation:

Calculate the Interquartile Range

Determine the Outlier Limits

Answer: