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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Percentiles and Quantiles", "Median Calculation" ], "new_concepts": [], "current_concepts": [ "Percentiles and Quantiles", "Median Calculation", "Five-Number Summary" ] } ## Sort the dataset in ascending order Using the *Median Calculation* and *Percentiles and Quantiles* knowledge points $$ \begin{aligned} \text{Data (sorted, } N=25\text{): } & 13.80, 13.90, 14.20, 14.35, 14.60, \ & 15.05, 15.15, 15.20, 15.25, 15.25, \ & 15.30, 15.55, 15.80, 16.00, 16.30, \ & 16.35, 16.45, 17.55, 17.60, 17.70, \ & 18.45, 18.70, 19.05, 19.10, 19.40 \end{aligned} $$ ## Calculate the second quartile (Median, Q2) Using the *Median Calculation* knowledge point $$ \begin{aligned} &\text{Position of } Q_2 = \frac{25 + 1}{2} = 13\text{th value}\ &Q_2 = 15.80 \end{aligned} $$ ## Calculate the first quartile (Q1) Using the *Percentiles and Quantiles* knowledge point $$ \begin{aligned} &\text{Lower half (first 12 values): } 13.80 \text{ to } 15.55\ &\text{Position of } Q_1 = \frac{12 + 1}{2} = 6.5\text{th value}\ &Q_1 = \frac{15.05 + 15.15}{2} = 15.10 \end{aligned} $$ ## Calculate the third quartile (Q3) Using the *Percentiles and Quantiles* knowledge point $$ \begin{aligned} &\text{Upper half (last 12 values): } 16.00 \text{ to } 19.40\ &\text{Position of } Q_3 = 13 + 6.5 = 19.5\text{th value}\ &Q_3 = \frac{17.60 + 17.70}{2} = 17.65 \end{aligned} $$ The data set's first, second, and third quartiles are: $Q_1 =$ $15.10$ $Q_2 =$ $15.80$ $Q_3 =$ $17.65$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Percentiles and Quantiles" ] }

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Explanation:

Sort the dataset in ascending order

Calculate the second quartile (Median, Q2)

Calculate the first quartile (Q1)

Calculate the third quartile (Q3)

Answer: