find interquartile range (iqr), the upper limit of the outlier, and lower limit of the outlier.

iqr = 4, upper limit of the outlier = 15, lower limit of the outlier = -1
iqr = 8, upper limit of the outlier = 12, lower limit of the outlier = -6

Question

find interquartile range (iqr), the upper limit of the outlier, and lower limit of the outlier.

iqr = 4, upper limit of the outlier = 15, lower limit of the outlier = -1
iqr = 8, upper limit of the outlier = 12, lower limit of the outlier = -6

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": [ "Interquartile Range", "Outlier Limits", "Box and Whisker Plot" ] } ## Calculate the Interquartile Range (IQR) Using the *Interquartile Range* knowledge point $$ \begin{aligned} Q_1 &= 5\ Q_3 &= 9\ \text{IQR} &= Q_3 - Q_1 = 9 - 5 = 4 \end{aligned} $$ ## Calculate the outlier limits Using the *Outlier Limits* knowledge point $$ \begin{aligned} \text{Lower Limit} &= Q_1 - 1.5 \times \text{IQR} = 5 - 1.5 \times 4 = 5 - 6 = -1\ \text{Upper Limit} &= Q_3 + 1.5 \times \text{IQR} = 9 + 1.5 \times 4 = 9 + 6 = 15 \end{aligned} $$ ## Match with the correct option Using the *Box and Whisker Plot* knowledge point $$ \begin{aligned} &\text{IQR} = 4\ &\text{Upper limit of the outlier} = 15\ &\text{Lower limit of the outlier} = -1 \end{aligned} $$

(A) IQR = 4, Upper limit of the outlier = 15, lower limit of the outlier = -1

(B) IQR = 8, Upper limit of the outlier = 12, lower limit of the outlier = -6

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

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QUESTION IMAGE

Question

Explanation:

Calculate the Interquartile Range (IQR)

Calculate the outlier limits

Match with the correct option

Answer: