recognizing outliers in a table

\begin{array}{|c|c|}
\hline x & y \\
\hline 0.5 & 41 \\
\hline 1 & 35 \\
\hline 1.5 & 37 \\
\hline 1.5 & 36 \\
\hline 2 & 35 \\
\hline 2.25 & 30 \\
\hline 2.75 & 31 \\
\hline
\end{array}

the data set in the table forms a cluster and does not include outliers.

which point, if added to the table, would be an outlier?

- (0.5, 42)
- (1.25, 35)
- (2.75, 41)
- (3.25, 28)

Question

recognizing outliers in a table

\begin{array}{|c|c|}
\hline x & y \\
\hline 0.5 & 41 \\
\hline 1 & 35 \\
\hline 1.5 & 37 \\
\hline 1.5 & 36 \\
\hline 2 & 35 \\
\hline 2.25 & 30 \\
\hline 2.75 & 31 \\
\hline
\end{array}

the data set in the table forms a cluster and does not include outliers.

which point, if added to the table, would be an outlier?

- (0.5, 42)
- (1.25, 35)
- (2.75, 41)
- (3.25, 28)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Bivariate Outliers" ], "new_concepts": [], "current_concepts": [ "Bivariate Outliers", "Scatterplot Properties" ] } ## Analyze the existing data cluster $$ \begin{aligned} &\text{Domain of } x: [0.5, 2.75] \ &\text{Range of } y: [30, 41] \ &\text{Trend: As } x \text{ increases, } y \text{ generally decreases (negative correlation).} \end{aligned} $$ ## Evaluate the given options against the trend $$ \begin{aligned} &(0.5, 42): \text{Fits the trend (low } x \text{, high } y\text{) and is very close to existing point } (0.5, 41). \ &(1.25, 35): \text{Fits the trend (middle } x \text{, middle } y\text{) and lies within the cluster.} \ &(2.75, 41): \text{Does not fit. For } x = 2.75\text{, the cluster } y \text{ values are around } 30\text{--}31\text{. A } y \text{ value of } 41 \text{ is far above the trend.} \ &(3.25, 28): \text{Fits the trend (higher } x \text{, lower } y\text{) continuing the downward slope.} \end{aligned} $$ ## Identify the outlier $$ \text{Outlier} = (2.75, 41) $$

(0.5, 42)

(1.25, 35)

(2.75, 41)

(3.25, 28)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Bivariate Outliers" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the existing data cluster

Evaluate the given options against the trend

Identify the outlier

Answer: