in a sample of 60 households, one house is worth $2,500,000. half of the rest are worth $280,000, and all the others are worth $315,000. which is the better measure of the \center\: the mean or the median?

mad

median

Question

in a sample of 60 households, one house is worth $2,500,000. half of the rest are worth $280,000, and all the others are worth $315,000. which is the better measure of the \center\: the mean or the median?

mad

median

mad

median

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": [ "Outlier Effects", "Measures of Center" ], "new_concepts": [], "current_concepts": [ "Outlier Effects", "Measures of Center" ] } ## Analyze the data distribution Using the *Measures of Center* knowledge point $$ \begin{aligned} &\text{Total households } (N) = 60\ &\text{Outlier value} = \$2,500,000 \quad (1 \text{ house})\ &\text{Remaining households} = 60 - 1 = 59\ &\text{Households worth } \$280,000 = \frac{59}{2} = 29.5 \approx 29 \text{ or } 30\ &\text{Households worth } \$315,000 = 59 - 29 = 30 \end{aligned} $$ ## Evaluate the effect of the outlier Using the *Outlier Effects* knowledge point $$ \begin{aligned} &\text{Outlier } (\$2,500,000) \gg \text{Typical values } (\$280,000 \text{ and } \$315,000)\ &\text{Mean is highly sensitive to extreme outliers.}\ &\text{Median is resistant to extreme outliers.} \end{aligned} $$

MAD

Median

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Measures of Center" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the data distribution

Evaluate the effect of the outlier

Answer: