question 5 (multiple choice worth 10 points)
(01.03h mc)

the table shows the number of goals made by two hockey players during the seasons games.

\begin{tabular}{|l|l|}
\hline
\textbf{player a} & \textbf{player b} \\
\hline
2, 3, 1, 3, 2, 2, 1, 3, 6 & 1, 4, 5, 1, 2, 4, 5, 5, 11 \\
\hline
\end{tabular}

which measure of variability is best for the data, and which player is more consistent?

- player a is the most consistent, with an iqr of 1.5.
- player b is the most consistent, with an iqr of 3.5.
- player a is the most consistent, with a standard deviation of 1.4.
- player b is the most consistent, with a standard deviation of 2.9.

Question

question 5 (multiple choice worth 10 points)
(01.03h mc)

the table shows the number of goals made by two hockey players during the seasons games.

\begin{tabular}{|l|l|}
\hline
\textbf{player a} & \textbf{player b} \\
\hline
2, 3, 1, 3, 2, 2, 1, 3, 6 & 1, 4, 5, 1, 2, 4, 5, 5, 11 \\
\hline
\end{tabular}

which measure of variability is best for the data, and which player is more consistent?

- player a is the most consistent, with an iqr of 1.5.
- player b is the most consistent, with an iqr of 3.5.
- player a is the most consistent, with a standard deviation of 1.4.
- player b is the most consistent, with a standard deviation of 2.9.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Outlier Detection", "Interquartile Range" ], "new_concepts": [ "Measures of Variability", "Data Consistency" ], "current_concepts": [ "Outlier Detection", "Interquartile Range", "Measures of Variability", "Data Consistency" ] } ## Identify outliers in the datasets $$ \begin{aligned} &\text{Player A: } 1, 1, 2, 2, 2, 3, 3, 3, 6 \quad (n = 9) \ &Q_1 = 1.5, \quad Q_3 = 3, \quad \text{IQR} = 1.5 \ &\text{Outlier boundary: } Q_3 + 1.5 \times \text{IQR} = 3 + 2.25 = 5.25 \implies 6 \text{ is an outlier.} \ &\text{Player B: } 1, 1, 2, 4, 4, 5, 5, 5, 11 \quad (n = 9) \ &Q_1 = 1.5, \quad Q_3 = 5, \quad \text{IQR} = 3.5 \ &\text{Outlier boundary: } Q_3 + 1.5 \times \text{IQR} = 5 + 5.25 = 10.25 \implies 11 \text{ is an outlier.} \end{aligned} $$ ## Determine the best measure of variability $$ \begin{aligned} &\text{Presence of outliers } (6 \text{ and } 11) \implies \text{IQR is the best measure of variability.} \end{aligned} $$ ## Compare consistency using IQR $$ \begin{aligned} &\text{IQR}_A = 1.5 < \text{IQR}_B = 3.5 \ &\implies \text{Player A is more consistent with an IQR of } 1.5. \end{aligned} $$

(A) Player A is the most consistent, with an IQR of 1.5.

(B) Player B is the most consistent, with an IQR of 3.5.

(C) Player A is the most consistent, with a standard deviation of 1.4.

(D) Player B is the most consistent, with a standard deviation of 2.9.

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

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QUESTION IMAGE

Question

Explanation:

Identify outliers in the datasets

Determine the best measure of variability

Compare consistency using IQR

Answer: