Question

samuel surveys 15 students at his school and asks them: \how many candies per day do you usually eat?\
samuel uses his results to make the following box plot.

what are the summary values given by this box plot?

minimum number of candies:
maximum number of candies:
range:
median number of candies:
interquartile range:

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Box Plots"
],
"new_concepts": [
"Five-number Summary",
"Interquartile Range"
],
"current_concepts": [
"Box Plots",
"Five-number Summary",
"Interquartile Range"
]
}
</pre_analysis>

<reasoning>

Identify five-number summary values from the box plot

\[

$$\begin{aligned} &\text{Minimum} = 0 \\ &\text{Lower Quartile } (Q_1) = 1 \\ &\text{Median } (Q_2) = 4 \\ &\text{Upper Quartile } (Q_3) = 6 \\ &\text{Maximum} = 13 \end{aligned}$$

\]

Calculate range and interquartile range

\[

$$\begin{aligned} &\text{Range} = \text{Maximum} - \text{Minimum} = 13 - 0 = 13 \\ &\text{Interquartile range (IQR)} = Q_3 - Q_1 = 6 - 1 = 5 \end{aligned}$$

\]
</reasoning>

<answer>
What are the summary values given by this box plot?

Minimum number of candies: <blank>0</blank>

Maximum number of candies: <blank>13</blank>

Range: <blank>13</blank>

Median number of candies: <blank>4</blank>

Interquartile range: <blank>5</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Statistics",
"Box Plots"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Box Plots"
],
"new_concepts": [
"Five-number Summary",
"Interquartile Range"
],
"current_concepts": [
"Box Plots",
"Five-number Summary",
"Interquartile Range"
]
}
</pre_analysis>

<reasoning>

Identify five-number summary values from the box plot

\[

$$\begin{aligned} &\text{Minimum} = 0 \\ &\text{Lower Quartile } (Q_1) = 1 \\ &\text{Median } (Q_2) = 4 \\ &\text{Upper Quartile } (Q_3) = 6 \\ &\text{Maximum} = 13 \end{aligned}$$

\]

Calculate range and interquartile range

\[

$$\begin{aligned} &\text{Range} = \text{Maximum} - \text{Minimum} = 13 - 0 = 13 \\ &\text{Interquartile range (IQR)} = Q_3 - Q_1 = 6 - 1 = 5 \end{aligned}$$

\]
</reasoning>

<answer>
What are the summary values given by this box plot?

Minimum number of candies: <blank>0</blank>

Maximum number of candies: <blank>13</blank>

Range: <blank>13</blank>

Median number of candies: <blank>4</blank>

Interquartile range: <blank>5</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Statistics",
"Box Plots"
]
}
</post_analysis>