Question

en nuestro conjunto de datos, ¿cuál fue el único valor atípico?
23, 34, 27, 12, 30, 26, 28, 31, 34

options:
12
12.5
44.5

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Interquartile Range",
"Outlier Boundaries"
],
"new_concepts": [],
"current_concepts": [
"Interquartile Range",
"Outlier Boundaries"
]
}
</pre_analysis>

<reasoning>

Ordenar el conjunto de datos y encontrar la mediana

\[
\text{Datos ordenados: } 12, 23, 26, 27, 28, 30, 31, 34, 34
\]
\[
N = 9 \implies \text{Mediana } (Q_2) = 28
\]

Calcular los cuartiles \(Q_1\) y \(Q_3\) e \(IQR\)

\[
\text{Mitad inferior: } 12, 23, 26, 27 \implies Q_1 = \frac{23 + 26}{2} = 24.5
\]
\[
\text{Mitad superior: } 30, 31, 34, 34 \implies Q_3 = \frac{31 + 34}{2} = 32.5
\]
\[
IQR = Q_3 - Q_1 = 32.5 - 24.5 = 8
\]

Determinar los límites para valores atípicos

\[
\text{Límite inferior} = Q_1 - 1.5 \times IQR = 24.5 - 1.5 \times 8 = 24.5 - 12 = 12.5
\]
\[
\text{Límite superior} = Q_3 + 1.5 \times IQR = 32.5 + 1.5 \times 8 = 32.5 + 12 = 44.5
\]
\[
12 < 12.5 \implies 12 \text{ es un valor atípico.}
\]
</reasoning>

<answer>
<mcq-correct>12</mcq-correct>
<mcq-option>12.5</mcq-option>
<mcq-option>44.5</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Statistics",
"Outlier Boundaries"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Interquartile Range",
"Outlier Boundaries"
],
"new_concepts": [],
"current_concepts": [
"Interquartile Range",
"Outlier Boundaries"
]
}
</pre_analysis>

<reasoning>

Ordenar el conjunto de datos y encontrar la mediana

\[
\text{Datos ordenados: } 12, 23, 26, 27, 28, 30, 31, 34, 34
\]
\[
N = 9 \implies \text{Mediana } (Q_2) = 28
\]

Calcular los cuartiles \(Q_1\) y \(Q_3\) e \(IQR\)

\[
\text{Mitad inferior: } 12, 23, 26, 27 \implies Q_1 = \frac{23 + 26}{2} = 24.5
\]
\[
\text{Mitad superior: } 30, 31, 34, 34 \implies Q_3 = \frac{31 + 34}{2} = 32.5
\]
\[
IQR = Q_3 - Q_1 = 32.5 - 24.5 = 8
\]

Determinar los límites para valores atípicos

\[
\text{Límite inferior} = Q_1 - 1.5 \times IQR = 24.5 - 1.5 \times 8 = 24.5 - 12 = 12.5
\]
\[
\text{Límite superior} = Q_3 + 1.5 \times IQR = 32.5 + 1.5 \times 8 = 32.5 + 12 = 44.5
\]
\[
12 < 12.5 \implies 12 \text{ es un valor atípico.}
\]
</reasoning>

<answer>
<mcq-correct>12</mcq-correct>
<mcq-option>12.5</mcq-option>
<mcq-option>44.5</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Statistics",
"Outlier Boundaries"
]
}
</post_analysis>